Question 25

In ΔPQR measure of angle Q is $$90^\circ$$. If $$cot P = \frac{8}{15}$$, and PQ = 4cm, then what is the length (in cm) of side PR?

Solution

Given : PQ = 4 cm and $$cot P = \frac{8}{15}$$

To find : PR = ?

Solution : In right $$\triangle$$ PQR,

=> $$cot(P)=\frac{PQ}{QR}$$

=> $$\frac{8}{15}=\frac{4}{QR}$$

=> $$QR=\frac{15}{8}\times4=7.5$$ cm

$$\therefore$$ $$(PR)^2=(PQ)^2+(QR)^2$$

=> $$(PR)^2=(4)^2+(7.5)^2$$

=> $$(PR)^2=16+56.25=72.25$$

=> $$PR=\sqrt{72.25}=8.5$$ cm

=> Ans - (A)

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