Question

For questions 1 - 6, solve the given triangles by finding the missing angle and other side lengths please help!!!

Answer 1

Answer:

m<B = 28°

$AB = 19.2$

$AC = 27.6$

Step-by-step explanation:

Given:

m<A = 112°

m<C = 40°

AC = 14

Required:

Find, m<B, AB and BC.

SOLUTION:

✍️m<B = 180° - (112° + 40°) (sum of ∆)

m<B = 28°

✍️Using sine rule, find AB.

$\frac{AB}{sin(C)} = \frac{AC}{sin(B)}$

Plug in the values into the equation.

$\frac{AB}{sin(40)} = \frac{14}{sin(28)}$

Cross multiply

$AB*sin(28) = 14*sin(40)$

Divide both sides by sin(28)

$AB = \frac{14*sin(40)}{sin(28)}$

$AB = 19.2$ (nearest tenth)

✍️Using sine rule, find BC.

$\frac{BC}{sin(A)} = \frac{AC}{sin(B)}$

Plug in the values into the equation.

$\frac{BC}{sin(112)} = \frac{14}{sin(28)}$

Cross multiply

$AC*sin(28) = 14*sin(112)$

Divide both sides by sin(28)

$AC = \frac{14*sin(112)}{sin(28)}$

$AC = 27.6$ (nearest tenth)