Question

Find all the missing elements

Answer 1

A = 23°

b = 9.5

c = 14.7

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:

`(sin(A))/(a) = (sin(B))/(b)`

Plug in the values

`(sin(23))/(7) = (sin(32))/(b)`

Cross multiply

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

Divide both sides by sin(23)

`b = (sin(32)*7)/(sin(23))`

b = 9.5 (nearest tenth)

✔️Find c using Law of Sines:

`(sin(A))/(a) = (sin(C))/(c)`

Plug in the values

`(sin(23))/(7) = (sin(125))/(c)`

Cross multiply

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

Divide both sides by sin(23)

`c = (sin(125)*7)/(sin(23))`

c = 14.7 (nearest tenth)