Question

$\text{The angles of a triangle are in the ratio 3 : 5 : 10. Then, the ratio of the smallest side to the greatest side is}$

• A. 1 : sin 10°
• B. 1 : 2 sin 10°
• C. 1 : cos 10°
• D. 1 : 2 cos 10°

Answer 1

The correct option is D

1 : 2 cos 10°

$\text{Let the angles of a triangle are 3x, 5x and 10x.}\therefore 3x+5x+10x={180}^0\Rightarrow x={10}^0\therefore \text{Smallest angle of a triangle}={30}^0\text{and the greatest angle}={100}^0\text{Required ratio}=sin{30}^0:sin{100}^0=1/2:cos{10}^0=1:2cos{10}^0$