Question

PLS HELP ASAP:Find all the missing elements:

Answer 1

B = 34.2°

C = 105.8°

c = 12.0 units

Explanation:

Given:

A = 40°

a = 8

b = 7

Required:

Find B, C, and c.

SOLUTION:

Using the Law of Sines, find <B:

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

`(sin(40))/(8) = (sin(B))/(7)`

Multiply both sides by 7

`(sin(40))/(8)*7 = (sin(B))/(7)*7`

`(sin(40)*7)/(8) = sin(B)`

`0.5624 = sin(B)`

`B = sin^(-1)(0.5624)`

`B = 34.2` (to nearest tenth).

Find <C:

C = 180 - (34.2+40°) (sum of angles in a triangle)

C = 180 - 74.2 = 105.8°

Using the Law of Sines, find c.

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

`(c)/(sin(105.8)) = (7)/(sin(34.2))`

Multiply both sides by sin(105.8)

`(c)/(sin(105.8))*sin(105.8) = (7)/(sin(34.2))*sin(105.8)`

`c = (7*sin(105.8))/(sin(34.2))`

`c = 12.0`