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

m∠B = 60°

b = 26 units

c = 30 units

Explanation:

In a right triangle ACB,

By applying Sine rule,

`\frac{\text{SinA}}{a}=\frac{\text{SinB}}{b}=(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}`

`(1)/(30)=\frac{\text{Sin90}}{c}=\frac{\text{Sin60}}{b}`

`(1)/(30) =(1)/(c)=((√(3))/(2))/(b)`

`(1)/(30)=(1)/(c)=(√(3))/(2b)`

`(1)/(30) =(1)/(c)` ⇒ c = 30 units

`(1)/(30)=(√(3))/(2b)`

b = 15√3

b = 25.98

b ≈ 26 units