Question

Please help me please.

In △ABC, m∠A=23 △ A B C , m ∠ A = 23 °, a=12 a = 12 , and b=15 b = 15 . Find c c to the nearest tenth.
A. 24.3
B. 14.4
C. 19.5
D. 26.5

Answer 1

we know that

Step 1

Find B

Applying the law of sines

a /sinA=b /sin B------> solve for sin B

sin B=(b/a)*sin A------> sin B=(15/12)*sin 23-----> sin B=0.4884

B=arc sin(0.4884)--------> B=29.2°

Step 2

Find C

we know that

A+B+C=180°

C=180-(23+29.2)-------> C=127.8°

Step 3

Find c

a /sinA=c /sin C------> solve for c

c=a*sin C/sin A-------> c=12*sin 127.8/sin 23------>c=24.3 units

the answer is

24.3