Find the measure of the indicated side or angle.

Question

asked May 25, 2022 180k views

1 Answer

Dhiraj Sharma · Answer 1 · 2022-05-30T21:28:47+0000

Given:

The given figure of a right triangle.

To find:

The length of PQ.

Solution:

In a right triangle,

$\tan \theta=(Perpendicular)/(Base)$

In right triangle QRS,

$\tan S=(QR)/(RS)$

$\tan (31+12)^\circ=(QR)/(6.3)$

$\tan 43^\circ=(QR)/(6.3)$

0.932515* 6.3=QR

5.8748445=QR

In right triangle PRS,

$\tan PSR=(PR)/(RS)$

$\tan 31^\circ=(PR)/(6.3)$

0.60086* 6.3=PR

3.785418=PR

Now,

PQ=QR-PR

PQ=5.8748445-3.785418

PQ=2.0894265

$PQ\approx 2$

Therefore, the measure of PQ is 2 cm.