Post on 10-Feb-2016
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5-Minute Check on Lesson 7-55-Minute Check on Lesson 7-5 Transparency 7-6
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Name the angles of depression and elevation in the two figures.1. 2.
3. Find the angle of elevation of the sun when a 6-meter flag pole casts a 17-meter shadow.
4. After flying at an altitude of 575 meters, a helicopter starts to descend when its ground distance from the landing pad is 13.5 Km. What is the angle of depression for this part of the flight?
5. The top of a signal tower is 250 feet above sea level. The angle of depression for the tope of the tower to a passing ship is 19°. How far is the foot of the tower from the ship?
6. From a point 50 feet from the base of a tree, the angle of elevation to the top of the tree is 32°. From a point closer to the base of the tree, the angle of elevation is 64°. Which of the following is the best estimate of the distance between the two points at which the angle of elevation is measured?A CB D15 28 29 35
URT; STR
about 19.4°
about 2.4°
about 726 ft
FED; CDE
D
U
T
R
S
F E
CDA B
Lesson 7-6
Law of Sines
Objectives• Use the Law of Sines to solve triangles
• Solve problems by using the Law of Sines
Vocabulary
• Solving a triangle – means finding the measures of all sides and all angles
Law of Sines A
B C
Let ∆ABC be any triangle with a, b and c representing the measures of the sides opposite the angles with measures A, B, and C respectively. Then
a
bc
sin A sin B sin C–––––– = –––––– = –––––– a b c
Law of Sines can be used to find missing parts of triangles that are not right triangles
Case 1: measures of two angles and any side of the triangle (AAS or ASA)
Case 2: measures of two sides and an angle opposite one of the known sides of the triangle (SSA)
Example 1Find p. Round to the nearest tenth.
Law of Sines
Use a calculator.
Divide each side by sin
Cross products
Answer:
Example 2
Law of Sines
Cross products
Divide each side by 7.
to the nearest degree in ,
Answer:
Solve for L.
Use a calculator.
a. Find c.
b. Find mT to the nearest degree in RST if r = 12, t = 7, and mT = 76.
Example 3
Answer:
Answer:
Example 4
We know the measures of two angles of the triangle. Use the Angle Sum Theorem to find
. Round angle measures to the nearest degree and side measures to the nearest tenth.
Angle Sum Theorem
Subtract 120 from each side.
Add.
Example 4 cont
To find d:
Law of Sines
Cross products
Substitute.
Use a calculator.
Divide each side by sin 8°.
Example 4 contTo find e:
Law of Sines
Cross products
Substitute.
Use a calculator.
Divide each side by sin 8°.
Answer:
Example 5
We know the measure of two sides and an angle opposite one of the sides.
Law of Sines
Cross products
Round angle measures to the nearest degree and side measures to the nearest tenth.
Example 5 cont
Solve for L.
Angle Sum Theorem
Use a calculator.
Add.
Substitute.
Divide each side by 16.
Subtract 116 from each side.
Example 5 cont
Cross products
Use a calculator.
Law of Sines
Divide each side by sin
Answer:
Answer:
a. Solve Round angle measures to the nearest degree and side
measures to the nearest tenth.
b. Round angle measures to the nearest degree and side measures to the nearest tenth.
Example 6
Answer:
Example 7A 46-foot telephone pole tilted at an angle of from the vertical casts a shadow on the ground. Find the length of the shadow to the nearest foot when the angle of elevation to the sun is
Draw a diagram Draw Then find the
Example 7 cont
Cross products
Use a calculator.
Law of Sines
Answer: The length of the shadow is about 75.9 feet.
Divide each side by sin
Since you know the measures of two angles of the triangle, and the length of a side opposite one of the angles you can use the Law of Sines to find the length of the shadow.
Example 8A 5-foot fishing pole is anchored to the edge of a dock. If the distance from the foot of the pole to the point where the fishing line meets the water is 45 feet, about how much fishing line that is cast out is above the surface of the water?
Answer: About 42 feet of the fishing line that is cast out is above the surface of the water.
Summary & Homework
• Summary:– Law of Sines can be used to solve for angles and
sides in triangles that are not right triangles– Case 1: measures of two angles and any side of the
triangle (AAS or ASA)– Case 2: measures of two sides and an angle
opposite one of the known sides of the triangle (SSA)
• Homework: – pg 380-381; 1, 4-7, 17-21, 30, 32