Question

Find the measure of the indicated side or angle.

Answer 1

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.