If the angles of a triangle are in the ratio $3 : 5 : 10$ then the ratio of smallest side to greatest side is

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

$1 : \sin 10^{0}$

$1 : 2 \sin 10^{0}$

$1 : \cos 10^{0}$

$1 : 2 \cos 10^{0}$

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given $A : B : C = 3 : 5 : 10$

Here $A$ is smallest angles and $C$ is longest angles

$A + B + C = 180 °$

So that $A = 30 °, C = 100 °$

Hence, the opposite sides are smalles and longest

$\begin{array}{rcl} \frac{a}{c} & = & \frac{2 R \sin A}{2 R \sin B} \\ = & \frac{\sin 30 °}{\sin 100 °} \\ = & \frac{1}{2 \cos 10 °} \end{array}$

Therefore, the ratio of shortest and longest side is $1 : 2 \cos 10 °$

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE