In △PQR, find the measure of ∡P. Triangle PQR where angle Q is a right angle. QR measures 33 point 8. PR measures 57 point 6. Measure of angle P is unknown. 30.4° 35.9° 59.6° 54…

Question

asked Sep 28, 2018 84.2k views

2 Answers

Blauharley · Answer 1 · 2018-10-02T12:49:28+0000

Answer:

∠P = 35.9°

Explanation:

We are given,

A right triangle PQR with ∠Q = 90°, QR = 33.8 and PR = 57.6.

Now, as we know,

In a right triangle, the angles can be written in terms of trigonometric functions.

So, we have,
$\sin P=(Perpendicular)/(Hypotenuse)$

We have that, QR is the perpendicular side and PR is the hypotenuse.

Thus,

$\sin P=(33.8)/(57.6)$

i.e.
$\sin P=0.5868$

i.e.
$P=\arcsin 0.5868$

i.e.
P=35.9

Thus, the measure of ∠P is 35.9°.