Given:
The given figure of a right triangle.
To find:
The length of PQ.
Solution:
In a right triangle,
[tex]\tan \theta=\dfrac{Perpendicular}{Base}[/tex]
In right triangle QRS,
[tex]\tan S=\dfrac{QR}{RS}[/tex]
[tex]\tan (31+12)^\circ=\dfrac{QR}{6.3}[/tex]
[tex]\tan 43^\circ=\dfrac{QR}{6.3}[/tex]
[tex]0.932515\times 6.3=QR[/tex]
[tex]5.8748445=QR[/tex]
In right triangle PRS,
[tex]\tan PSR=\dfrac{PR}{RS}[/tex]
[tex]\tan 31^\circ=\dfrac{PR}{6.3}[/tex]
[tex]0.60086\times 6.3=PR[/tex]
[tex]3.785418=PR[/tex]
Now,
[tex]PQ=QR-PR[/tex]
[tex]PQ=5.8748445-3.785418[/tex]
[tex]PQ=2.0894265[/tex]
[tex]PQ\approx 2[/tex]
Therefore, the measure of PQ is 2 cm.
