Question

PLEASE HELP ASAPPPP!!!


Solve the right triangle given that mA =30°, mC = 90° and a = 15. Then round your result to ONE decimal place

Answer 1

Answer:

m∠B = 60°

b = 26 units

c = 30 units

Step-by-step explanation:

In a right triangle ACB,

By applying Sine rule,

$\frac{\text{SinA}}{a}=\frac{\text{SinB}}{b}=\frac{SinC}{c}$

m∠A = 30°, m∠C = 90°

m∠A + m∠B + m∠C = 180°

30° + m∠B + 90° = 180°

m∠B = 180° - 120°

m∠B = 60°

Therefore, $\frac{\text{Sin30}}{15}=\frac{\text{Sin90}}{c}=\frac{\text{Sin60}}{b}$

$\frac{1}{30}=\frac{\text{Sin90}}{c}=\frac{\text{Sin60}}{b}$

$\frac{1}{30} =\frac{1}{c}=\frac{\frac{\sqrt{3}}{2}}{b}$

$\frac{1}{30}=\frac{1}{c}=\frac{\sqrt{3}}{2b}$

$\frac{1}{30} =\frac{1}{c}$ ⇒ c = 30 units

$\frac{1}{30}=\frac{\sqrt{3}}{2b}$

b = 15√3

b = 25.98

b ≈ 26 units