Question

Solve △ABC given that C=32°, b=8, and a=3. Round the answer to the nearest hundredth.

A. A = 16.22°, B = 131.78°, c = 5.68
B. A = 99.72°, B = 48.28°, c = 5.68
C. A = 48.28°, B= 99.72°, c = 8.54
D. A = 131.78°, B = 16.22°, c = 8.54

Answer 1

Angle A is approximately 16.22°, angle B is approximately 131.78°, and side c is approximately 5.68.

Step-by-step explanation:

To solve △ABC, we can use the law of sines. The law of sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant. In this case, we have the angles C = 32° and sides b = 8 and a = 3. Using the law of sines, we can find angle A:

Sin(A) / 3 = Sin(32°) / 8

Then we can solve for angle A:

Sin(A) = (3 * Sin(32°)) / 8

A = arcsin((3 * Sin(32°)) / 8)

Using a calculator, we find A ≈ 16.22°. Angle B can be found by subtracting angles A and C from 180°:

B = 180° - 32° - 16.22°

Using a calculator, we find B ≈ 131.78°. Finally, side c can be found using the law of sines:

c / Sin(C) = 3 / Sin(16.22°)

Then we can solve for c:

c = (Sin(32°) * 3) / Sin(16.22°)

Rounding to the nearest hundredth, we find c ≈ 5.68.