Question

PLS HELP ASAP:Find all the missing elements:

Answer 1

Answer:

B = 34.2°

C = 105.8°

c = 12.0 units

Step-by-step Explanation:

Given:

A = 40°

a = 8

b = 7

Required:

Find B, C, and c.

SOLUTION:

Using the Law of Sines, find <B:

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

$\frac{sin(40)}{8} = \frac{sin(B)}{7}$

Multiply both sides by 7

$\frac{sin(40)}{8}*7 = \frac{sin(B)}{7}*7$

$\frac{sin(40)*7}{8} = sin(B)$

$0.5624 = sin(B)$

$B = sin^{-1}(0.5624)$

$B = 34.2$ (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.

$\frac{c}{sin(C)} = \frac{b}{sin(B)}$

$\frac{c}{sin(105.8)} = \frac{7}{sin(34.2)}$

Multiply both sides by sin(105.8)

$\frac{c}{sin(105.8)}*sin(105.8) = \frac{7}{sin(34.2)}*sin(105.8)$

$c = \frac{7*sin(105.8)}{sin(34.2)}$

$c = 12.0$