Question 74

In the given figure, if PQ = 13 cm and PR = 12 cm, then the value of $$\sin \theta + \tan \theta =$$ ?

Solution

Given, $$PQ$$ = 13 cm  and  $$PR$$ = 12 cm

By Pythagoras theorem,

$$QR^2+PR^2=PQ^2$$

$$=$$>  $$QR^2+12^2=13^2$$

$$=$$>  $$QR^2+144=169$$

$$=$$>  $$QR^2=25$$

$$=$$>  $$QR=5$$ cm

From the right angled traingle $$PQR$$,

$$\sin\theta\ =\frac{PR}{PQ}$$

$$=$$> $$\sin\theta\ =\frac{5}{13}$$

$$\tan\theta\ =\frac{PR}{QR}$$

$$=$$> $$\tan\theta\ =\frac{5}{12}$$

$$\therefore\ \sin\theta\ +\tan\theta\ =\frac{12}{13}+\frac{12}{5}=\frac{60+156}{65}=\frac{216}{65}$$

Hence, the correct answer is Option B


Create a FREE account and get:

  • Free SSC Study Material - 18000 Questions
  • 230+ SSC previous papers with solutions PDF
  • 100+ SSC Online Tests for Free

cracku

Boost your Prep!

Download App