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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
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1. Find the angle of elevation of the sun when a 6-meter flagpole casts a 17-meter shadow.
2. 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?
3. 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?
• Law of Sines• solving a triangle
• Use the Law of Sines to solve triangles.• Solve problems by using the Law of Sines.
Use the Law of Sines
Law of Sines
Use a calculator.
Divide each side by sin
Cross products
Answer: p ≈ 4.8
Use the Law of Sines
B. Find mL to the nearest degree in ΔLMN if n = 7, ℓ = 9, and mN = 43.
Law of Sines
Cross products
Divide each side by 7.
Use the Law of Sines
Answer: mL ≈ 61
Solve for L.
Use a calculator.
A. AB. BC. CD. D
A. 4.6
B. 29.9
C. 7.8
D. 8.5
A. Find c to the nearest tenth.
A. AB. BC. CD. D
A. 34
B. 67
C. 70
D. 44
B. Find mT to the nearest degree in ΔRST if r = 12, t = 7, and mR = 76.
Solve Triangles
A. Solve ΔDEF if mD = 8, mF = 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
Solve Triangles
Angle Sum Theorem
Subtract 120 from each side.
Add.
Since we know and f, use proportions involving
Solve Triangles
To find d:
Law of Sines
d sin 112° = 12 sin 8° Cross products
Substitute.
Use a calculator.
Divide each side by sin 112°.
d ≈ 1.8
Solve Triangles
Answer: mE = 60; d ≈ 1.8; e ≈ 11.2
To find e:
Law of Sines
e sin 112° = 12 sin 60° Cross products
Substitute.
Use a calculator.
Divide each side by sin 112°.
Solve Triangles
B. Solve ΔHJK if mJ = 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
Solve Triangles
83.5° = HUse a calculator.84 ≈ mH mH + mJ + mK = 180Angle Sum Theorem84 + 32 + mK = 180Substitute.116 + mK = 180Add. mK ≈ 64Subtract 116 from each side.
Solve Triangles
Answer: mH ≈ 84; mK ≈ 64; k ≈ 27.3
k sin 32° = 16 sin 64° Cross products
Use a calculator.
Law of Sines
Divide each side by sin
k ≈ 27.3
mJ = 32, mK = 64, j = 16
1. A2. B3. C4. D
A. 60
B. 68
C. 34
D. 146
A. For ΔRST, mR = 43, mT = 103, and r = 14. Find mS. Round measures to the nearest degree and side measures to the nearest tenth.
1. A2. B3. C4. D
A. 17.1
B. 9.8
C. 11.5
D. 20.0
B. For ΔRST, mR = 43, mT = 103, and r = 14. Find s. Round measures to the nearest degree and side measures to the nearest tenth.
1. A2. B3. C4. D
A. 17.1
B. 9.8
C. 11.5
D. 20.0
C. For ΔRST, mR = 43, mT = 103, and r = 14. Find t. Round measures to the nearest degree and side measures to the nearest tenth.
1. A2. B3. C4. D
A. 49
B. 31
C. 65
D. 6
D. For ΔTUV, mT = 43, t = 12, and v = 9. Find mV. Round measures to the nearest degree and side measures to the nearest tenth.
1. A2. B3. C4. D
A. 88
B. 72
C. 131
D. 106
E. For ΔTUV, mT = 43, t = 12, and v = 9. Find mU. Round measures to the nearest degree and side measures to the nearest tenth.
1. A2. B3. C4. D
A. 16.9
B. 13.2
C. 16.7
D. 17.6
F. For ΔTUV, mT = 43, t = 12, and v = 9. Find u. Round measures to the nearest degree and side measures to the nearest tenth.
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°.
Indirect Measurement
Draw a diagram Draw Then find the
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.
Answer: The length of the shadow is to about 75.9 feet.
Indirect Measurement
Cross products
Use a calculator.
Law of Sines
Divide each side by sin
1. A2. B3. C4. D
A. about 48 feet
B. about 42 feet
C. about 39 feet
D. about 36 feet
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?
