Question

How would I figure this one out?

Answer 1

Explanation:

Considering the given triangle, to determine b, we would apply the sine rule. It is expressed as

SinA/a = SinB/b = SinC/c

Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. Likening it to the given triangle, the expression becomes

Sin x/12 = Sin75/22

Cross multiplying, it becomes

22Sinx = 12 × 0.966 = 11.592

Sinx = 11.592/22 = 0.5269

x = Sin^- 1(0.5269)

x = 31.8 to the nearest tenth

Answer 2

x = 31.8°

Explanation:

We simply have to replace in the sine law with the values ​​that we can see in the problem

the side that corresponds to angle A will always be the one opposite to the angle (it does not touch this angle) and the same with B and C

Law of sines: Sin A / a = Sin B / b = Sin C / c

A = 75°

a = 22cm

B = x

b = 12cm

Sin 75° / 22 = Sin x / 12

(Sin 75° / 22) * 12 = Sin x

Sin ^-1 [(Sin (75°) / 22) * 12] = x

31.79° = x

if we round to the nearest tenth

x = 31.79° = 31.8°