1. Find the angle of elevation of the sun when a 6-meter flagpole 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 kilometers. 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 from the top of the tower to a passing ship is 19°. How far is the foot of the tower from the ship?
Lesson 6 Menu

2. Use the Law of Sines to solve triangles.
Solve problems by using the Law of Sines.
Law of Sines
solving a triangle
Lesson 6 MI/Vocab

3. Lesson 6 KC1

4. A. Find p. Round to the nearest tenth.
Use the Law of Sines
A. Find p. Round to the nearest tenth.
Lesson 6 Ex1

5. Use the Law of Sines Law of Sines Cross products
Divide each side by sin
Use a calculator.
Answer: p ≈ 4.8
Lesson 6 Ex1

6. Use the Law of Sines
B. Find mL to the nearest degree in ΔLMN if n = 7, ℓ = 9, and mN = 43.
Law of Sines
Cross products
Divide each side by 7.
Lesson 6 Ex1

7. Use the Law of Sines Solve for L. Use a calculator. Answer: mL ≈ 61
Lesson 6 Ex1

8. A. Find c to the nearest tenth.
B. 29.9
C. 7.8
D. 8.5 A B C D
Lesson 6 CYP1

9. B. Find mT to the nearest degree in ΔRST if r = 12, t = 7, and mR = 76.
C. 70
D. 44 A B C D
Lesson 6 CYP1

10. Solve Triangles
A. Solve ΔDEF if mD = 8, mF = 112, and f = 12. 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
Lesson 6 Ex2

11. Subtract 120 from each side.
Solve Triangles
Angle Sum Theorem
Add.
Subtract 120 from each side.
Since we know and f, use proportions involving
Lesson 6 Ex2

12. d sin 112° = 12 sin 8° Cross products
Solve Triangles
To find d:
Law of Sines
Substitute.
d sin 112° = 12 sin 8° Cross products
Divide each side by sin 112°.
d ≈ 1.8
Use a calculator.
Lesson 6 Ex2

13. e sin 112° = 12 sin 60° Cross products
Solve Triangles
To find e:
Law of Sines
Substitute.
e sin 112° = 12 sin 60° Cross products
Divide each side by sin 112°.
Use a calculator.
Answer: mE = 60; d ≈ 1.8; e ≈ 11.2
Lesson 6 Ex2

14. 30 sin 32° = 16 sin H Cross products
Solve Triangles
B. Solve ΔHJK if mJ = 32, h = 30, and j = 16. Round angle measures to the nearest degree and side measures to the nearest tenth.
30 sin 32° = 16 sin H Cross products
Lesson 6 Ex2

15. mH + mJ + mK = 180 Angle Sum Theorem
Solve Triangles
83.5° = H Use a calculator.
84 ≈ mH
mH + mJ + mK = 180 Angle Sum Theorem
mK = 180 Substitute.
116 + mK = 180 Add.
mK ≈ 64 Subtract 116 from each side.
Lesson 6 Ex2

16. k sin 32° = 16 sin 64° Cross products
Solve Triangles
Law of Sines
mJ = 32, mK = 64, j = 16
k sin 32° = 16 sin 64° Cross products
Divide each side by sin
k ≈ 27.3
Use a calculator.
Answer: mH ≈ 84; mK ≈ 64; k ≈ 27.3
Lesson 6 Ex2

17. A. For ΔRST, mR = 43, mT = 103, and r = 14. Find mS
A. For ΔRST, mR = 43, mT = 103, and r = 14. Find mS. Round measures to the nearest degree and side measures to the nearest tenth.
A. 60
B. 68
C. 34
D. 146 A B C D
Lesson 6 CYP2

18. B. For ΔRST, mR = 43, mT = 103, and r = 14. Find s
B. For ΔRST, mR = 43, mT = 103, and r = 14. Find s. Round measures to the nearest degree and side measures to the nearest tenth.
A. 17.1
B. 9.8
C. 11.5
D. 20.0 A B C D
Lesson 6 CYP2

19. C. For ΔRST, mR = 43, mT = 103, and r = 14. Find t
C. For ΔRST, mR = 43, mT = 103, and r = 14. Find t. Round measures to the nearest degree and side measures to the nearest tenth.
A. 17.1
B. 9.8
C. 11.5
D. 20.0 A B C D
Lesson 6 CYP2

20. D. For ΔTUV, mT = 43, t = 12, and v = 9. Find mV
D. For ΔTUV, mT = 43, t = 12, and v = 9. Find mV. Round measures to the nearest degree and side measures to the nearest tenth.
A. 49
B. 31
C. 65
D. 6 A B C D
Lesson 6 CYP2

21. E. For ΔTUV, mT = 43, t = 12, and v = 9. Find mU
E. For ΔTUV, mT = 43, t = 12, and v = 9. Find mU. Round measures to the nearest degree and side measures to the nearest tenth.
A. 88
B. 72
C. 131
D. 106 A B C D
Lesson 6 CYP2

22. F. For ΔTUV, mT = 43, t = 12, and v = 9. Find u
F. For ΔTUV, mT = 43, t = 12, and v = 9. Find u. Round measures to the nearest degree and side measures to the nearest tenth.
A. 16.9
B. 13.2
C. 16.7
D. 17.6 A B C D
Lesson 6 CYP2

23. Draw a diagram Draw Then find the
Indirect Measurement
A 46-foot telephone pole tilted at an angle of 7° 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 33°.
Draw a diagram Draw Then find the
Lesson 6 Ex3

24. Indirect Measurement
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.
Lesson 6 Ex3

25. Answer: The length of the shadow is to about 75.9 feet.
Indirect Measurement
Law of Sines
Cross products
Divide each side by sin
Use a calculator.
Answer: The length of the shadow is to about 75.9 feet.
Lesson 6 Ex3

26. A fishing pole is anchored to the edge of a dock
A 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?
A. about 48 feet
B. about 42 feet
C. about 39 feet
D. about 36 feet A B C D
Lesson 6 CYP3

27. Lesson 6 KC2