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In triangle $$\triangle{PQR}$$, we have $$\angle P = 90^\circ$$$$QR = 20$$, and $$\tan R = 4\sin R$$. What is $$PR$$?

Aug 5, 2020

#1
+31296
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This is a right-angled triangle with QR as the hypotenuse.  Let PQ be the Opposite to angle at R, and PR be the Adjacent.

tanR = 4sinR  means 1/cosR = 4, or cosR = 1/4

But cosR = PR/QR = PR/20

So PR/20 = 1/4

Hence PR = 5

Aug 5, 2020
#2
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