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Transparency 7-6
5-Minute Check on Lesson 7-5
Name the angles of depression and elevation in the two figures. 2.
3. Find the angle of elevation of the sun when a 6-meter flag pole casts a 17-meter shadow.
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?
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?
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? F E C D A B U T R S
URT; STR
FED; CDE
about 19.4°
about 2.4°
about 726 ft A 15 B 28 C 29 D D 35
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2. Lesson 7-6
Law of Sines

3. Objectives Use the Law of Sines to solve triangles
Solve problems by using the Law of Sines

4. Vocabulary
Solving a triangle – means finding the measures of all sides and all angles

5. Law of Sines sin A sin B sin C 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 c b B C a
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)

6. Example 1 Find p. Round to the nearest tenth. Law of Sines
Cross products
Divide each side by sin
Use a calculator.
Answer:

7. Example 2 to the nearest degree in , Law of Sines Cross products
Divide each side by 7.
Solve for L.
Use a calculator.
Answer:

8. Example 3
a. Find c.
b. Find mT to the nearest degree in RST if r = 12, t = 7, and mT = 76.
Answer:
Answer:

9. Example 4
. Round angle measures to the nearest degree and side measures to the nearest tenth.
We know the measures of two angles of the triangle. Use the Angle Sum Theorem to find
Angle Sum Theorem
Add.
Subtract 120 from each side.

10. Example 4 cont To find d: Law of Sines Substitute. Cross products
Divide each side by sin 8°.
Use a calculator.

11. Example 4 cont To find e: Law of Sines Substitute. Cross products
Divide each side by sin 8°.
Use a calculator.
Answer:

12. Example 5
Round angle measures to the nearest degree and side measures to the nearest tenth.
We know the measure of two sides and an angle opposite one of the sides.
Law of Sines
Cross products

13. Example 5 cont Divide each side by 16. Solve for L. Use a calculator.
Angle Sum Theorem
Substitute.
Add.
Subtract 116 from each side.

14. Example 5 cont Law of Sines Cross products Divide each side by sin
Use a calculator.
Answer:

15. Example 6
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.
Answer:
Answer:

16. Example 7
A 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

17. Example 7 cont
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.
Law of Sines
Cross products
Divide each side by sin
Use a calculator.
Answer: The length of the shadow is about 75.9 feet.

18. Example 8
A 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.

19. Summary & Homework Summary: Homework:
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 ; 1, 4-7, 17-21, 30, 32