Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The sides of a triangle are in the ratio $1: \sqrt{3} : 2$. Then the angles are in the ratio

TS EAMCET 2017

Solution:

We have,
Ratio of sides of triangle are $1: \sqrt{3}: 2$.
Let the sides are $k, \sqrt{3} k, 2 k$
image
Since, this triangle is a right angle triangle
$(2 k)^{2}=(\sqrt{3} k)^{2}+(k)^{2}=(2 k)^{2}$
$\therefore \sin A=\frac{\sqrt{3} k}{2 k}=\frac{\sqrt{3}}{2} \Rightarrow A=60^{\circ}$
$\Rightarrow \sin C=\frac{k}{2 k}=\frac{1}{2} \Rightarrow C=30^{\circ}$
$\Rightarrow B=90^{\circ}$
$\therefore $ Ratio of angles are $30^{\circ}: 60^{\circ}: 90^{\circ}$
$\Rightarrow 1: 2: 3$