Find the values of the variables.
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Transcript of Find the values of the variables.
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Warm-Up Exercises
Find the values of the variables.
1.
ANSWER x = 2 6, y = 2 15
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Warm-Up Exercises
Find the values of the variables.
2.
ANSWER 15 2
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Warm-Up ExercisesEXAMPLE 1 Find tangent ratios
Find tan S and tan R. Write each answer as a fraction and as a decimal rounded to four places.
SOLUTION
tan S =opp S
adj. to S= RT
ST= 80
18= 40
9 4.4444
tan R =opp R
adj. to R= ST
RT= 18
80= 9
400.2250=
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Warm-Up ExercisesGUIDED PRACTICE for Example 1
Find tan J and tan K. Round to four decimal places.
ANSWER 0.7500, 1.3333 ANSWER 0.5333, 1.8750
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Warm-Up ExercisesEXAMPLE 2 Find a leg length
ALGEBRA Find the value of x.
SOLUTIONUse the tangent of an acute angle to find a leg length.
tan 32o=
opp. adj. Write ratio for tangent of 32o.
tan 32o 11
=x
Substitute.
x tan 32o = 11 Multiply each side by x.
x = 11 tan 32o Divide each side by tan 32o
x 11 0.6249
Use a calculator to find tan 32o
x 17.6 Simplify
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Warm-Up ExercisesEXAMPLE 3 Estimate height using tangent
LAMPPOST
Find the height h of the lamppost to the nearest inch.
tan 70o=
opp. adj.
Write ratio for tangent of 70o.
tan 70o h
=40
Substitute.
40 tan 70o = hMultiply each side by 40.
109.9 h Use a calculator to simplify.
ANSWER
The lamppost is about 110 inches tall.
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Warm-Up ExercisesEXAMPLE 4 Use a special right triangle to find a tangent
Use a special right triangle to find the tangent of a 60o angle.
STEP 1
Because all 30o-60o-90o triangles are similar, you can simplify your calculations by choosing 1 as the length of the shorter leg. Use the 30o-60o-90o Triangle Theorem to find the length of the longer leg.
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Warm-Up ExercisesEXAMPLE 4 Use a special right triangle to find a tangent
longer leg = shorter leg 3 30o- 60o- 90o Triangle Theorem
x = 1
3 Substitute.
x = 3 Simplify.
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Warm-Up ExercisesEXAMPLE 4 Use a special right triangle to find a tangent
STEP 2
tan 60o =opp. adj.
Write ratio for tangent of 60o.
tan 60o =3
1Substitute.
tan 60o = 3 Simplify.
ANSWER
The tangent of any 60o angle is 3 1.7321
Find tan 60o
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Warm-Up ExercisesGUIDED PRACTICE for Examples 2, 3, and 4
Find the value of x. Round to the nearest tenth.
ANSWER 12.2 ANSWER 19.3
ANSWER
shorter leg = 5, longer leg = , 35 tan 60 = 5
5 3 = 3
What If? In Example 4, suppose the side length of the shorter leg is 5 instead of 1. Show that the tangent of 60° is still equal to .
5.
3
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Warm-Up ExercisesDaily Homework Quiz
1. If a = 18, b = 80 and c = 81, find tan B and tan A. Write each answer as a fraction and a decimal rounded to 4 places.
Use this diagram for Exercises 1- 4.
ANSWER tan B = 409
= 4.4444; tan A = = 0.2250940
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Warm-Up ExercisesDaily Homework Quiz
Use this diagram for Exercises 1- 4.
2. If a = 17 and m A = 31 , find b to the nearest tenth.o
ANSWER 28.3
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Warm-Up ExercisesDaily Homework Quiz
Use this diagram for Exercises 1- 4.
3. If a = 9 and m B = 74 , find b to the nearest tenth.o
ANSWER 31.4
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Warm-Up ExercisesDaily Homework Quiz
Use this diagram for Exercises 1- 4.
ANSWER 64.3
4. If a = 5 and m B = 11 , find the number of square units in the area of ABC to the nearest tenth.
o