Question

If the length of side a is 12 centimeters, m∠B = 36°, and m∠C = 75°, what is the length of side b? Round your response to two decimal places.

Answer 1

if the length of side a=12 centimeters
m< B=36° and
m< C=75°
To solve an AAS triangle
use the three angles add to 180° to find the other angle
then The Law of Sines to find each of the other two sides

m< A=180-%2836%2B75%29=69°

using The Law of Sines:
a%2Fsin+%28A%29+=b%2Fsin+%28B%29+=+c%2Fsin%28+C%29=>





we use:
12%2Fsin+%2869%29=+b%2Fsin%2836%29+

12%2F0.93=+b%2F0.59
12.9=+b%2F0.59
b=12.9%2A0.59
b=7.61cm-the length of side b

Answer 2

It was 7.56