Question

Solve the right triangle given that mZA= 30°, mZC = 90°, anda = 15. Round your result to one decimal place.​

Answer 1

Answer:

$\angle B = 60^o$

$b =17.3$

$c = 20$

Step-by-step explanation:

Given

$a= 15$

$\angle A = 30^o$

$\angle C = 90^o$

See attachment for illustration

Required

Solve the triangle

First, we calculate the measure of B

$\angle A + \angle B + \angle C = 180^o$ --- angles in a triangle

$30^o + \angle B + 90^o = 180^o$

Collect like terms

$\angle B = 180^o-90^o-30^o$

$\angle B = 60^o$

Solve for (c) using sine function

$\sin(30) = \frac{a}{c}$

Make c the subject

$c = \frac{a}{\sin(30)}$

Substitute known values

$c = \frac{10}{0.5}$

$c = 20$

Solve for (b) using Pythagoras

$c^2 = a^2 + b^2$

This gives:

$20^2 = 10^2 + b^2$

$400 = 100 + b^2$

Collect like terms

$b^2 =400 - 100$

$b^2 =300$

Take square roots

$b =17.3$