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,

$\tan \theta=\dfrac{Perpendicular}{Base}$

In right triangle QRS,

$\tan S=\dfrac{QR}{RS}$

$\tan (31+12)^\circ=\dfrac{QR}{6.3}$

$\tan 43^\circ=\dfrac{QR}{6.3}$

$0.932515\times 6.3=QR$

$5.8748445=QR$

In right triangle PRS,

$\tan PSR=\dfrac{PR}{RS}$

$\tan 31^\circ=\dfrac{PR}{6.3}$

$0.60086\times 6.3=PR$

$3.785418=PR$

Now,

$PQ=QR-PR$

$PQ=5.8748445-3.785418$

$PQ=2.0894265$

$PQ\approx 2$

Therefore, the measure of PQ is 2 cm.