Question

Find all the missing elements

Answer 1

Answer:

A = 23°

b = 9.5

c = 14.7

Step-by-step explanation:

B = 32°

C = 125°

a = 7

✔️Find A:

A = 180° - (B + C) (sum of triangle)

A = 180° - (32° + 125°)

A = 23°

✔️Find b using Law of Sines:

$\frac{sin(A)}{a} = \frac{sin(B)}{b}$

Plug in the values

$\frac{sin(23)}{7} = \frac{sin(32)}{b}$

Cross multiply

$sin(23)*b = sin(32)*7$

Divide both sides by sin(23)

$b = \frac{sin(32)*7}{sin(23)}$

b = 9.5 (nearest tenth)

✔️Find c using Law of Sines:

$\frac{sin(A)}{a} = \frac{sin(C)}{c}$

Plug in the values

$\frac{sin(23)}{7} = \frac{sin(125)}{c}$

Cross multiply

$sin(23)*c = sin(125)*7$

Divide both sides by sin(23)

$c = \frac{sin(125)*7}{sin(23)}$

c = 14.7 (nearest tenth)