Answer:
Step-by-step explanation:
We are given the triangle ABC and told to find ∠A, ∠B, and side b. Also we are told that side c= 54 . side a=64 and ∠C = 32°
we need law of sines a / sin A = b / sin B = c / sin C
let's use law of sines to find the other angles
64 / sin A = 54 / sin(32)
I'm just going to swap the fractions on both sides , just to make it easier
sin A / 64 = sin(32) / 54
∠A = arcSin(64 * sin(32) / 54)
∠A = 38.9066°
∠B + ∠A + ∠C = 180
∠B = 180 - 32 - 38.9066
∠B = 109.0934°
let's find side b now
sin B / b = sin(32) / 54
sin(109.0934°) / b = sin(32) / 54
54 * sin(109.0934°) / sin(32) = b
96.2963 = b
