If the length of side a is 12 centimeters, mZB = 36°, and mZC = 75°, what is the length of side b?

Round your response to two decimal places.

b = 7.56 cm

Step-by-step explanation:

Sum of the angles in a triangle = 180

so m∠A = 180 - 75 - 36 = 69;

use the law of sines:

(sin A) / a = (sin B) / b = (sin C) / C.

Now plug in ∠A = 69 into formula (sin A) / a = (sin B) / b and solve for b:

(sin 69) / 12 = (sin 36) / b

cross multiply:

b sin 69 = 12 sin 36 divide each side by sin 69

b = {12 sin 36} / sin 69

b = (12 sin 36) / sin 69 = 7.555 ...

b = 7.56