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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
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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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thanks admin!

 Aug 5, 2020
 #3
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*moderator

Inspirational  Aug 6, 2020

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