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Question

In PQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Find the value of sin P.


A
1213
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B
1214
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C
0.9231
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D
0.8571
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Solution

The correct options are
A 1213
C 0.9231

We are given

PR + QR = 25 cm

or PR = (25 – QR) cm

By Pythagoras theorem,

PR2 = QR2 + PQ2

or (25QR)2 = QR2 + 52

or 625 + QR2 – 50 QR = QR2 + 25

or 50 QR = 625 – 25 = 600

or QR = 12 cm.

and PR = (25 – 12) cm = 13 cm

Now sin P = QRPR = 1213


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