Question

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

Answer 1

AB = 15

m ∠A = 53.1°

m ∠B = 36.9°

Explanation:

`AB^2 = AC^2+CB^2 \\AB^2 = 9^2 + 12^2 = 81 + 144 = 225\\AB = √(225) = 15`

`sin A = (opposite)/(hypotenuse) = (12)/(15)\\\\A = sin^(-1) ((12)/(15))\\\\`

A = 53.13

m∠A = 53.1°

∠A + ∠B + ∠C = 180°

53.1 +∠B + 90 = 180

∠B = 180 - 90 - 53.1 = 36.9°

Answer 2

AB² = AC²+BC²

AB² = 9²+12²

AB²= 225

AB= 15

SinA = 12/15

A = Sin-¹(0.8)

M`A = 53°

M`B = 90- A = 90-53= 37°