Question

Find all the missing elements : C=120degrees

b= 5
c=11

Answer 1

A = 36.8°

B = 23.2°

a = 7.6

Explanation:

Given:

C = 120°

b = 5

c = 11

Required:

Find A, B, and a.

Solution:

✔️To find B, apply the Law of Sines

`(sin(B))/(b) = (sin(C))/(c)`

Plug in the values

`(sin(B))/(5) = (sin(120))/(11)`

Cross multiply

Sin(B)*11 = sin(120)*5

Divide both sides by 11

`sin(B) = (sin(120)*5)/(11)`

`sin(B) = (sin(120)*5)/(11)`

Sin(B) = 0.3936

B =
`sin^(-1)(0.3936)`

B = 23.1786882° ≈ 23.2° (nearest tenth)

✔️Find A:

A = 180° - (B + C) (sum of triangle)

A = 180° - (23.2° + 120°)

A = 36.8°

✔️To find a, apply the Law of sines:

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

Plug in the values

`(sin(36.8))/(a) = (sin(23.2))/(5)`

Cross multiply

a*sin(23.2) = 5*sin(36.8)

Divide both sides by sin(23.2)

a = 7.60294329 ≈ 7.6 (nearest tenth)