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Question
In ΔPQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.
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Solution
Given that, PR + QR = 25
PQ = 5
Let PR be x.
Therefore, QR = 25 − x
Applying Pythagoras theorem in ΔPQR, we obtain
PR2 = PQ2 + QR2
x2 = (5)2 + (25 − x)2
x2 = 25 + 625 + x2 − 50x
50x = 650
x = 13
Therefore, PR = 13 cm
QR = (25 − 13) cm
= 12 cm
sin P = `("QR")/("PR")=12/13`
cos P = `("PQ")/("PR")=5/13`
tan P = `("QR")/("PQ")=12/5`
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