Question

GIVING 50 POINTS!!!

Solve the triangle using the law of sines. Show all work and round answers to the nearest tenth.

Answer 1

• a = 27, ∠A = 28°, ∠B = 7°

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Use the law of sines:

• a/sin ∠A = b/sin ∠B = c/sin ∠C

Use the given values and find the measure of angle B:

• 7/sin ∠B = 33/sin 145°
• sin ∠B = 7 sin 145°/33
• sin ∠B = 0.12166
• ∠B = arcsin (0.12166)
• ∠B = 7° (rounded)

We have now two angle measures.

Use triangle sum theorem to find the third angle:

• ∠A + ∠B + ∠C = 180°
• ∠A + 7° + 145° = 180°
• ∠A + 152° = 180°
• ∠A = 28°

Find the last side length:

• a/sin ∠A = b/sin ∠B
• a/sin 28° = 7/sin 7°
• a = 7 sin 28° / sin 7°
• a = 27.0 (rounded)