11-1 Square Roots and Irrational Numbers PRE-ALGEBRA LESSON 11-1 A blue cube is 3 times as tall as a...
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Transcript of 11-1 Square Roots and Irrational Numbers PRE-ALGEBRA LESSON 11-1 A blue cube is 3 times as tall as a...
11-1
Square Roots and Irrational NumbersSquare Roots and Irrational NumbersPRE-ALGEBRA LESSON 11-1PRE-ALGEBRA LESSON 11-1
A blue cube is 3 times as tall as a red cube. How many red cubes canfit into the blue cube?
27
Square Roots and Irrational NumbersSquare Roots and Irrational NumbersPRE-ALGEBRA LESSON 11-1PRE-ALGEBRA LESSON 11-1
(For help, go to Lesson 4-2.)
Write the numbers in each list without exponents.
1. 12, 22, 32, . . ., 122 2. 102, 202, 302, . . ., 1202
Check Skills You’ll Need
11-1
Square Roots and Irrational NumbersSquare Roots and Irrational NumbersPRE-ALGEBRA LESSON 11-1PRE-ALGEBRA LESSON 11-1
Solutions
1. 12, 22, 32, . . . , 122
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
2. 102, 202, 302, . . . , 1202
100, 400, 900, 1,600, 2,500, 3,600, 4,900, 6,400, 8,100, 10,000, 12,100, 14,400
11-1
b. – 81
Square Roots and Irrational NumbersSquare Roots and Irrational Numbers
Simplify each square root.
PRE-ALGEBRA LESSON 11-1PRE-ALGEBRA LESSON 11-1
a. 144
144 = 12
– 81 = – 9
Quick Check
11-1
Square Roots and Irrational NumbersSquare Roots and Irrational NumbersPRE-ALGEBRA LESSON 11-1PRE-ALGEBRA LESSON 11-1
You can use the formula d = 1.5h to estimate the
distance d, in miles, to a horizon line when your eyes are h feet
above the ground. Estimate the distance to the horizon seen by a
lifeguard whose eyes are 20 feet above the ground.
The lifeguard can see about 5 miles to the horizon.
Find the square root of the closest perfect square.
25 = 5
Use the formula.d = 1.5h
Replace h with 20.d = 1.5(20)
Multiply.d = 30
Find perfect squares close to 30.25 30 36< <
Quick Check
11-1
c. 3
a. 49
Square Roots and Irrational NumbersSquare Roots and Irrational Numbers
Identify each number as rational or irrational. Explain.
PRE-ALGEBRA LESSON 11-1PRE-ALGEBRA LESSON 11-1
rational, because 49 is a perfect square
rational, because it is a terminating decimal
irrational, because 3 is not a perfect square
rational, because it is a repeating decimal
irrational, because 15 is not a perfect square
rational, because it is a terminating decimal
irrational, because it neither terminates nor repeats
e. – 15
g. 0.1234567 . . .
f. 12.69
d. 0.3333 . . .
b. 0.16
Quick Check
11-1
Simplify each square root or estimate to the nearest integer.
1. – 100 2. 57
Identify each number as rational or irrational.
3. 48 4. 0.0125
5. The formula d = 1.5h , where h equals the height, in feet, of the viewer’s eyes, estimates the distance d, in miles, to the horizon
from the viewer. Find the distance to the horizon for a person whose eyes are 6 ft above the ground.
Square Roots and Irrational NumbersSquare Roots and Irrational NumbersPRE-ALGEBRA LESSON 11-1PRE-ALGEBRA LESSON 11-1
irrational
–10 8
rational
3 mi
11-1
11-2
The Pythagorean TheoremThe Pythagorean TheoremPRE-ALGEBRA LESSON 11-2PRE-ALGEBRA LESSON 11-2
The Jones’ Organic Farm has 18 tomato plants and 30 string beanplants. Farmer Jones wants every row to contain at least twotomato plants and two bean plants. There should be as many rowsas possible, and all the rows must be the same. How should FarmerJones plant the rows?
6 rows, with each row containing 5 bean plants and 3 tomato plants
The Pythagorean TheoremThe Pythagorean TheoremPRE-ALGEBRA LESSON 11-2PRE-ALGEBRA LESSON 11-2
(For help, go to Lesson 4-2.)
Simplify.
1. 42 + 62 2. 52 + 82
3. 72 + 92 4. 92 + 32
Check Skills You’ll Need
11-2
The Pythagorean TheoremThe Pythagorean TheoremPRE-ALGEBRA LESSON 11-2PRE-ALGEBRA LESSON 11-2
Solutions
1. 42 + 62 2. 52 + 82 16 + 36 = 52 25 + 64 = 89
3. 72 + 92 4. 92 + 32 49 + 81 = 130 81 + 9 = 90
11-2
The Pythagorean TheoremThe Pythagorean Theorem
Find c, the length of the hypotenuse.
PRE-ALGEBRA LESSON 11-2PRE-ALGEBRA LESSON 11-2
c2 = a2 + b2 Use the Pythagorean Theorem.
c2 = 1,225 Simplify.
c = 1,225 = 35 Find the positive square root of each side.
The length of the hypotenuse is 35 cm.
Replace a with 28, and b with 21.c2 = 282 + 212
Quick Check
11-2
The Pythagorean TheoremThe Pythagorean Theorem
Find the value of x in the triangle.
Round to the nearest tenth.
PRE-ALGEBRA LESSON 11-2PRE-ALGEBRA LESSON 11-2
x = 147
x2 = 147
Find the positive square root of each side.
Subtract 49 from each side.
a2 + b2 = c2
49 + x2 = 196
72 + x2 = 142
Use the Pythagorean Theorem.
Simplify.
Replace a with 7, b with x, and c with 14.
11-2
Then use one of the two methods below to approximate .147
The Pythagorean TheoremThe Pythagorean Theorem
(continued)
PRE-ALGEBRA LESSON 11-2PRE-ALGEBRA LESSON 11-2
The value of x is about 12.1 in.
Estimate the nearest tenth.x 12.1
Use the table on page 778. Find the number closest to 147 in the N2 column. Then find the corresponding value in the N column. It is a little over 12.
Method 2 Use a table of square roots.
Method 1 Use a calculator.
is 12.124356.A calculator value for 147
Round to the nearest tenth.x 12.1
Quick Check
11-2
The Pythagorean TheoremThe Pythagorean Theorem
The carpentry terms span, rise, and
rafter length are illustrated in the diagram.
A carpenter wants to make a roof that has a
span of 20 ft and a rise of 10 ft. What should
the rafter length be?
PRE-ALGEBRA LESSON 11-2PRE-ALGEBRA LESSON 11-2
The rafter length should be about 14.1 ft.
c2 = a2 + b2 Use the Pythagorean Theorem.
Round to the nearest tenth.c 14.1
Find the positive square root.c = 200
Add.c2 = 200
Square 10.c2 = 100 + 100
Replace a with 10 (half the span), and b with 10.c2 = 102 + 102
Quick Check
11-2
The Pythagorean TheoremThe Pythagorean Theorem
Is a triangle with sides 10 cm, 24 cm, and 26 cm
a right triangle?
PRE-ALGEBRA LESSON 11-2PRE-ALGEBRA LESSON 11-2
The triangle is a right triangle.
Simplify.100 + 576 676
Replace a and b with the shorter lengths and c with the longest length.
102 + 242 262
a2 + b2 = c2 Write the equation to check.
676 = 676
Quick Check
11-2
Find the missing length. Round to the nearest tenth.
1. a = 7, b = 8, c =
2. a = 9, c = 17, b =
3. Is a triangle with sides 6.9 ft, 9.2 ft, and 11.5 ft a right triangle? Explain.
4. What is the rise of a roof if the span is 30 ft and the rafter length is16 ft? Refer to the diagram on page 586.
The Pythagorean TheoremThe Pythagorean TheoremPRE-ALGEBRA LESSON 11-2PRE-ALGEBRA LESSON 11-2
about 5.6 ft
10.6
14.4
yes; 6.92 + 9.22 = 11.52
11-2
11-3
Distance and Midpoint FormulasDistance and Midpoint FormulasPRE-ALGEBRA LESSON 11-3PRE-ALGEBRA LESSON 11-3
Find the number halfway between 0.784 and 0.76.
0.772
Distance and Midpoint FormulasDistance and Midpoint FormulasPRE-ALGEBRA LESSON 11-3PRE-ALGEBRA LESSON 11-3
(For help, go to Lesson 1-10.)
Write the coordinates of each point.1. A 2. D 3. G 4. J
Check Skills You’ll Need
11-3
Distance and Midpoint FormulasDistance and Midpoint FormulasPRE-ALGEBRA LESSON 11-3PRE-ALGEBRA LESSON 11-3
Solutions
1. A (–3, 4) 2. D (0, 3) 3. G (–4, –2) 4. J (3, –1)
11-3
Distance and Midpoint FormulasDistance and Midpoint Formulas
Find the distance between T(3, –2) and V(8, 3).
PRE-ALGEBRA LESSON 11-3PRE-ALGEBRA LESSON 11-3
The distance between T and V is about 7.1 units.
Round to the nearest tenth.d 7.1
Find the exact distance.50d =
Simplify.d = 52 + 52
Replace (x2, y2) with (8, 3) and (x1, y1) with (3, –2).
d = (8 – 3)2 + (3 – (–2 ))2
Use the Distance Formula.d = (x2 – x1)2 + (y2 – y1)2
Quick Check
11-3
Distance and Midpoint FormulasDistance and Midpoint Formulas
Find the perimeter of WXYZ.
PRE-ALGEBRA LESSON 11-3PRE-ALGEBRA LESSON 11-3
The points are W (–3, 2), X (–2, –1), Y (4, 0), Z (1, 5). Use the Distance Formula to find the side lengths.
(–2 – (–3))2 + (–1 – 2)2WX =
1 + 9 = 10=
Replace (x2, y2) with (–2, –1) and (x1, y1) with (–3, 2).
Simplify.
(4 – (–2))2 + (0 – (–1)2XY =
36 + 1 == Simplify.37
Replace (x2, y2) with (4, 0) and (x1, y1) with (–2, –1).
11-3
Distance and Midpoint FormulasDistance and Midpoint Formulas
(continued)
PRE-ALGEBRA LESSON 11-3PRE-ALGEBRA LESSON 11-3
9 + 25 ==
(1 – 4)2 + (5 – 0)2YZ =
Simplify.
Replace (x2, y2) with (1, 5) and (x1, y1) with (4, 0).
34
(–3 – 1)2 + (2 – 5)2ZW =
Simplify.
Replace (x2, y2) with (–3, 2) and (x1, y1) with (1, 5).
= 16 + 9 = 25 = 5
11-3
Distance and Midpoint FormulasDistance and Midpoint Formulas
(continued)
PRE-ALGEBRA LESSON 11-3PRE-ALGEBRA LESSON 11-3
The perimeter is about 20.1 units.
perimeter = + + + 5 20.1343710
Quick Check
11-3
Distance and Midpoint FormulasDistance and Midpoint Formulas
Find the midpoint of TV.
PRE-ALGEBRA LESSON 11-3PRE-ALGEBRA LESSON 11-3
Use the Midpoint Formula.x1 + x2
2y1 + y2
2,
Replace (x1, y1) with (4, –3) and(x2, y2) with (9, 2).
= ,4 + 92
–3 + 22
Simplify the numerators.= ,132
–12
Write the fractions in simplest form.= 6 , –12
12
The coordinates of the midpoint of TV are 6 , – .12
12
Quick Check
11-3
Find the length (to the nearest tenth) and midpoint of each segment with the given endpoints.
1. A(–2, –5) and B(–3, 4) 2. D(–4, 6) and E(7, –2)
3. Find the perimeter of ABC, with coordinates A(–3, 0), B(0, 4), and C(3, 0).
Distance and Midpoint FormulasDistance and Midpoint FormulasPRE-ALGEBRA LESSON 11-3PRE-ALGEBRA LESSON 11-3
16
9.1; (–2 , – )12
12
13.6; (1 , 2)12
11-3
11-4
Problem Solving Strategy: Write a Proportion Problem Solving Strategy: Write a Proportion PRE-ALGEBRA LESSON 11-4PRE-ALGEBRA LESSON 11-4
Use these numbers to write as many proportions as you can: 5, 8, 15, 24
515
= 15 5
824
24 8
58
1524=, , 24
15= , 8
5=
Problem Solving Strategy: Write a Proportion Problem Solving Strategy: Write a Proportion PRE-ALGEBRA LESSON 11-4PRE-ALGEBRA LESSON 11-4
(For help, go to Lesson 6-2.)
Solve each proportion.
1. = 2. =
3. = 4. =
13
a12
h5
2025
14
8x
27
c35
Check Skills You’ll Need
11-4
Problem Solving Strategy: Write a Proportion Problem Solving Strategy: Write a Proportion PRE-ALGEBRA LESSON 11-4PRE-ALGEBRA LESSON 11-4
Solutions
1. = 2. =
3 • a = 1 • 12 25 • h = 5 • 20 3a = 12 25h = 100
a = 4 h = 4
3. = 4. =
1 • x = 4 • 8 7 • c = 2 • 35 x = 32 7c = 70
c = 10
13
a12
h5
2025
14
8x
27
c35
11-4
Problem Solving Strategy: Write a Proportion Problem Solving Strategy: Write a Proportion
At a given time of day, a building of unknown
height casts a shadow that is 24 feet long. At the same
time of day, a post that is 8 feet tall casts a shadow that is
4 feet long. What is the height x of the building?
PRE-ALGEBRA LESSON 11-4PRE-ALGEBRA LESSON 11-4
Since the triangles are similar, and you know three lengths, writing and solving a proportion is a good strategy to use. It is helpful to draw the triangles as separate figures.
11-4
Problem Solving Strategy: Write a Proportion Problem Solving Strategy: Write a Proportion
(continued)
PRE-ALGEBRA LESSON 11-4PRE-ALGEBRA LESSON 11-4
Write a proportion using the legs of the similar right triangles.
4x = 24(8) Write cross products.
4x = 192 Simplify.
x = 48 Divide each side by 4.
The height of the building is 48 ft.
= Write a proportion.8x
424
Quick Check
11-4
Write a proportion and solve.
1. On the blueprints for a rectangular floor, the width of the floor is 6 in. The diagonal distance across the floor is 10 in. If the width of the actual floor is 32 ft, what is the actual diagonal distance across the floor?
2. A right triangle with side lengths 3 cm, 4 cm, and 5 cm is similar to a right triangle with a 20-cm hypotenuse. Find the perimeter of the larger triangle.
3. A 6-ft-tall man standing near a geyser has a shadow 4.5 ft long. The geyser has a shadow 15 ft long. What is the height of the geyser?
Problem Solving Strategy: Write a Proportion Problem Solving Strategy: Write a Proportion PRE-ALGEBRA LESSON 11-4PRE-ALGEBRA LESSON 11-4
48 cm
about 53 ft
20 ft
11-4
11-5
Special Right TrianglesSpecial Right TrianglesPRE-ALGEBRA LESSON 11-5PRE-ALGEBRA LESSON 11-5
One angle measure of a right triangle is 75 degrees. What is the measurement, in degrees, of the other acute angle of the triangle?
15 degrees
Special Right TrianglesSpecial Right TrianglesPRE-ALGEBRA LESSON 11-5PRE-ALGEBRA LESSON 11-5
(For help, go to Lesson 11-2.)
Find the missing side of each right triangle.
1. legs: 6 m and 8 m 2. leg: 9 m; hypotenuse: 15 m
3. legs: 27 m and 36 m 4. leg: 48 m; hypotenuse: 60 m
Check Skills You’ll Need
11-5
Special Right TrianglesSpecial Right TrianglesPRE-ALGEBRA LESSON 11-5PRE-ALGEBRA LESSON 11-5
Solutions
1. c2 = a2 + b2 2. a2 + b2 = c2
c2 = 62 + 82 92 + b2 = 152
c2 = 100 81 + b2 = 225 c = 100 = 10 m b2 = 144
b = 144 = 12 m
3. c2 = a2 + b2 4. a2 + b2 = c2
c2 = 272 + 362 482 + b2 = 602
c2 = 2025 2304 + b2 = 3600 c = 2025 = 45 m b2 = 1296
b = 1296 = 36 m
11-5
Special Right TrianglesSpecial Right Triangles
Find the length of the hypotenuse in the triangle.
PRE-ALGEBRA LESSON 11-5PRE-ALGEBRA LESSON 11-5
hypotenuse = leg • 2 Use the 45°-45°-90° relationship.
y = 10 • 2 The length of the leg is 10.
The length of the hypotenuse is about 14.1 cm.
14.1 Use a calculator.
Quick Check
11-5
Special Right TrianglesSpecial Right TrianglesPRE-ALGEBRA LESSON 11-5PRE-ALGEBRA LESSON 11-5
Patrice folds square napkins diagonally to put on a
table. The side length of each napkin is 20 in. How long is the
diagonal?
hypotenuse = leg • 2 Use the 45°-45°-90° relationship.
y = 20 • 2 The length of the leg is 20.
The diagonal length is about 28.3 in.
28.3 Use a calculator.
Quick Check
11-5
Special Right TrianglesSpecial Right Triangles
Find the missing lengths in the triangle.
PRE-ALGEBRA LESSON 11-5PRE-ALGEBRA LESSON 11-5
The length of the shorter leg is 7 ft. The length of the longer leg is about 12.1 ft.
hypotenuse = 2 • shorter leg14 = 2 • b The length of the hypotenuse is 14.
= Divide each side by 2.
7 = b Simplify.
142
2b2
longer leg = shorter leg • 3
a = 7 • 3 The length of the shorter leg is 7.
a 12.1 Use a calculator.
Quick Check
11-5
Find each missing length.
1. Find the length of the legs of a 45°-45°-90° triangle with a hypotenuse of 4 2 cm.
2. Find the length of the longer leg of a 30°-60°-90° triangle with a hypotenuse of 6 in.
3. Kit folds a bandana diagonally before tying it around her head. The side length of the bandana is 16 in. About how long is the diagonal?
Special Right TrianglesSpecial Right TrianglesPRE-ALGEBRA LESSON 11-5PRE-ALGEBRA LESSON 11-5
4 cm
about 22.6 in.
3 3 in.
11-5
11-6
Sine, Cosine, and Tangent RatiosSine, Cosine, and Tangent RatiosPRE-ALGEBRA LESSON 11-6PRE-ALGEBRA LESSON 11-6
A piece of rope 68 in. long is to be cut into two pieces. How long will each piece be if one piece is cut three times longer than the other piece?
17 in. and 51 in.
Sine, Cosine, and Tangent RatiosSine, Cosine, and Tangent RatiosPRE-ALGEBRA LESSON 11-6PRE-ALGEBRA LESSON 11-6
(For help, go to Lesson 6-3.)
Solve each problem.
1. A 6-ft man casts an 8-ft shadow while a nearby flagpole casts a 20-ft shadow. How tall is the flagpole?
2. When a 12-ft tall building casts a 22-ft shadow, how long is the shadow of a nearby 14-ft tree?
Check Skills You’ll Need
11-6
Sine, Cosine, and Tangent RatiosSine, Cosine, and Tangent RatiosPRE-ALGEBRA LESSON 11-6PRE-ALGEBRA LESSON 11-6
Solutions
1. = 2. =
6 • 20 = 8 • x 22 • 14 = 12 • x
120 = 8x 308 = 12x
= =
x = 15 ft x = 25 ft
68
x20
1222
14x
1208
8x8
30812
12x12
23
11-6
Sine, Cosine, and Tangent RatiosSine, Cosine, and Tangent Ratios
Find the sine, cosine, and tangent of A.
PRE-ALGEBRA LESSON 11-6PRE-ALGEBRA LESSON 11-6
sin A = = = opposite
hypotenuse35
1220
cos A = = = adjacent
hypotenuse45
1620
tan A = = = oppositeadjacent
34
1216
Quick Check
11-6
Sine, Cosine, and Tangent RatiosSine, Cosine, and Tangent RatiosPRE-ALGEBRA LESSON 11-6PRE-ALGEBRA LESSON 11-6
Find the trigonometric ratios of 18° using a scientific
calculator or the table on page 779. Round to four decimal
places.
Scientific calculator: Enter 18 and pressthe key labeled SIN, COS, or TAN.
cos 18° 0.9511
tan 18° 0.3249
sin 18° 0.3090
Table: Find 18° in the first column. Lookacross to find the appropriate ratio.
Quick Check
11-6
Sine, Cosine, and Tangent RatiosSine, Cosine, and Tangent Ratios
The diagram shows a doorstop in the shape of a wedge. What is the length of the hypotenuse of the doorstop?
PRE-ALGEBRA LESSON 11-6PRE-ALGEBRA LESSON 11-6
You know the angle and the side opposite the angle. You want to find w, the length of the hypotenuse.
w(sin 40°) = 10 Multiply each side by w.
The hypotenuse is about 15.6 cm long.
w 15.6 Use a calculator.
sin A = Use the sine ratio.opposite
hypotenuse
sin 40° = Substitute 40° for the angle, 10 forthe height, and w for the hypotenuse.
10w
w = Divide each side by sin 40°.10
sin 40°
Quick Check
11-6
Solve.
1. In ABC, AB = 5, AC = 12, and BC = 13. If A is a right angle, find the sine, cosine, and tangent of B.
2. One angle of a right triangle is 35°, and the adjacent leg is 15. a. What is the length of the opposite leg?
b. What is the length of the hypotenuse?
3. Find the sine, cosine, and tangent of 72° using a calculator or a table.
Sine, Cosine, and Tangent RatiosSine, Cosine, and Tangent RatiosPRE-ALGEBRA LESSON 11-6PRE-ALGEBRA LESSON 11-6
about 10.5
about 18.3
1213
, ,513
125
sin 72° 0.9511; cos 72° 0.3090; tan 72° 3.0777
11-6
11-7
Angles of Elevation and DepressionAngles of Elevation and DepressionPRE-ALGEBRA LESSON 11-7PRE-ALGEBRA LESSON 11-7
An airplane flies at an average speed of 275 miles per hour. How far does the airplane fly in 150 minutes?
687.5 miles
Angles of Elevation and DepressionAngles of Elevation and DepressionPRE-ALGEBRA LESSON 11-7PRE-ALGEBRA LESSON 11-7
(For help, go to Lesson 2-3.)
Find each trigonometric ratio.
1. sin 45° 2. cos 32°
3. tan 18° 4. sin 68°
5. cos 88° 6. tan 84°
Check Skills You’ll Need
11-7
Angles of Elevation and DepressionAngles of Elevation and DepressionPRE-ALGEBRA LESSON 11-7PRE-ALGEBRA LESSON 11-7
Solutions
1. sin 45° 0.7071 2. cos 32° 0.8480
3. tan 18° 0.3249 4. sin 68° 0.9272
5. cos 88° 0.0349 6. tan 84° 9.5144
11-7
Angles of Elevation and DepressionAngles of Elevation and Depression
Janine is flying a kite. She lets out 30 yd of string
and anchors it to the ground. She determines that the angle
of elevation of the kite is 52°. What is the height h of the kite
from the ground?
PRE-ALGEBRA LESSON 11-7PRE-ALGEBRA LESSON 11-7
30(sin 52°) = h Multiply each side by 30.
The kite is about 24 yd from the ground.
Draw a picture.
24 h Simplify.
sin A = Choose an appropriate trigonometric ratio.
oppositehypotenuse
sin 52° = Substitute.h
30
Quick Check
11-7
Angles of Elevation and DepressionAngles of Elevation and DepressionPRE-ALGEBRA LESSON 11-7PRE-ALGEBRA LESSON 11-7
Greg wants to find the height of a tree. From his position 30
ft from the base of the tree, he sees the top of the tree at an angle of
elevation of 61°. Greg’s eyes are 6 ft from the ground. How tall is the
tree, to the nearest foot?
30(tan 61°) = h Multiply each side by 30.
54 + 6 = 60 Add 6 to account for the heightof Greg’s eyes from the ground.
The tree is about 60 ft tall.
Draw a picture.
54 h Use a calculator or a table.
Choose an appropriate trigonometric ratio.
oppositeadjacenttan A =
Substitute 61 for the angle measure and 30 for the adjacent side.
h30tan 61° =
Quick Check
11-7
Angles of Elevation and DepressionAngles of Elevation and Depression
An airplane is flying 1.5 mi above the ground. If the pilot must begin a 3° descent to an airport runway at that altitude, how far is the airplane from the beginning of the runway (in ground distance)?
PRE-ALGEBRA LESSON 11-7PRE-ALGEBRA LESSON 11-7
Draw a picture(not to scale).
d • tan 3° = 1.5 Multiply each side by d.
tan 3° = Choose an appropriate trigonometric ratio.1.5d
11-7
Angles of Elevation and DepressionAngles of Elevation and Depression
(continued)
PRE-ALGEBRA LESSON 11-7PRE-ALGEBRA LESSON 11-7
The airplane is about 28.6 mi from the airport.
= Divide each side by tan 3°.d • tan 3°tan 3°
1.5tan 3°
d = Simplify.1.5
tan 3°
d 28.6 Use a calculator.
Quick Check
11-7
Solve. Round answers to the nearest unit.
1. The angle of elevation from a boat to the top of a lighthouse is 35°. The lighthouse is 96 ft tall. How far from the base of the lighthouse is the boat?
2. Ming launched a model rocket from 20 m away. The rocket traveled straight up. Ming saw it peak at an angle of 70°. If she is 1.5 m tall, how high did the rocket fly?
3. An airplane is flying 2.5 mi above the ground. If the pilot must begin a 3° descent to an airport runway at that altitude, how far is the airplane from the beginning of the runway (in ground distance)?
Angles of Elevation and DepressionAngles of Elevation and DepressionPRE-ALGEBRA LESSON 11-7PRE-ALGEBRA LESSON 11-7
137 ft
57 m
48 mi
11-7