Question 25

ΔPQR is right angled at Q. If $$tan P = \frac{24}{7}$$, then what is the value of cos R ?

Solution

Given : $$\tan P$$ = $$\frac{24}{7}$$

Also, $$\tan P=\frac{QR}{PQ}=\frac{24}{7}$$

Let QR = 24 cm and PQ = 7 cm

Thus, in $$\triangle$$ PQR, => $$(PR)^2=(PQ)^2+(QR)^2$$

=> $$(PR)^2=(7)^2+(24)^2$$

=> $$(PR)^2=49+576=625$$

=> $$PR=\sqrt{625}=25$$ cm

To find : $$\cos R=\frac{QR}{PR}$$

= $$\frac{24}{25}$$

=> Ans - (B)

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