SSC CGL 2022 PYQ — Question 55

The correct answer is Option 2 i.e. $2{{4} \over 13}$.

In a right-angled triangle, $\tan\theta = {perpendicular \over base}$

$\sin\theta = {perpendicular\over hypotenuse}$

In triangle ABC, BC = 5, AC = 12, then using Pythagoras theorem, AB = 13.

Now, sinA = $BC \over AB$  = $5 \over 13$     ...(i)

sinB = ${AC \over AB} = {12 \over 13}$    ...(ii)

sinC = sin90° = 1     ...(iii)

Now, adding equations (i), (ii) and (iii), we get

sinA + sinB + sinC = ${5 \over 13} + {12 \over 13} + 1$ 

⇒ sinA + sinB + sinC = $(5 + 12 + 13) \over 13$ = $30 \over 13$ = $2 \frac{4}{13}$

Hence the value of sinA + sinB + sinC is $2 \frac{4}{13}$ .