Question

What is measure of angle P? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth. ° P Q R is a right triangle. Q is a right angle. P Q is equal to eight centimeters, Q R is equal to fifteen centimeters and P R is equal to seventeen centimeters.

Answer 1

61.93°

Explanation:

Using cosine law:

15² = 8² + 17² - 2(8)(17)cosP

225 = 353 - 272cosP

cosP = 8/17

P = 61.92751306

Answer 2

Given:

In ΔPQR, ∠Q = 90°

PQ = 8 cm

QR = 15 cm and

PR = 17 cm

To find the value of ∠P.

Formula

By Trigonometric ratio we get,

`tan \theta=(opp)/(adj)`

Now let us take ∠P = θ

With respect to θ, QR be the opposite side and PQ be the adjacent side.

So,

tan θ =
`(QR)/(PQ)`

tan θ =
`(15)/(8)`

θ =
`tan^(-1) ((15)/(8) )`

θ = 61.93° (approx)

Hence, the value of ∠P is 61.93° (approx).