Question

In triangle PQR, 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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Answer 1

Step-by-step explanation:

Given,

In triangle PQR,

PQ = 5cm

PR + QR = 25cm

Let us say, QR = x

Then, PR = 25 – QR = 25 – x

Using Pythagoras theorem:

PR² = PQ² + QR²

Now, substituting the value of PR, PQ and QR, we get;

(25-x)² = (5)² + (x)²

(25)²+x²-50x = 25 + x²

625 – 50 x = 25

50 x = 600

x = 12

So, QR = 12

PR = 25 – QR = 25 – 12 = 13

Therefore,

sin P = QR/PR = 12/13

cos P = PQ/pR = 5/13

tan P = QR/PQ = 12/5

Answer 2

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