Question

Solve the right triangle. Round decimal answers to the nearest tenth

Answer 1

AB = 15

m∠A = 53.1°

m∠B = 36.9°

Answer 2

AB = 15

m∠A = 53.1°

m∠B = 36.9°

Explanation:

From the picture attached,

By Applying Pythagoras theorem,

AB² = AC² + BC²

AB² = 9² + (12)²

AB² = 81 + 144

AB = √225

AB = 15

tan(B) =
`\frac{\text{Opposite side}}{\text{Adjacent side}}`

=
`(12)/(9)`

= 1.3333

B =
`\text{tan}^(-1)(1.3333)`

= 53.13

≈ 53.1°

Since, m∠A + m∠B + m∠C = 180°

m∠A + 53.1° + 90° = 180°

m∠A = 180°- 143.1°

= 36.9°