Answer:
m∠B ≈ 28.05°
Explanation:
Because we don't know whether this is a right triangle, we'll need to use the Law of Sines to find the measure of angle B (aka m∠B).
The Law of Sines relates a triangle's side lengths and the sines of its angles and is given by the following:
.
Thus, we can plug in 36 for C, 15 for c, and 12 for b to find the measure of angle B:
Step 1: Plug in values and simplify:
sin(36) / 15 = sin(B) / 12
0.0391856835 = sin(B) / 12
Step 2: Multiply both sides by 12:
(0.0391856835) = sin(B) / 12) * 12
0.4702282018 = sin(B)
Step 3: Take the inverse sine of 0.4702282018 to find the measure of angle B:
sin^-1 (0.4702282018) = B
28.04911063
28.05 = B
Thus, the measure of is approximately 28.05° (if you want or need to round more or less, feel free to).