Question

If the sides of a right angled triangle are in the ratio $1:\sqrt{3}:2$, then its angles are .

• A. 45° , 45° , 90°
• B. 30° , 60° , 90°
• C. 40° , 40° , 100°
• D. 30° , 30° , 120°

Answer 1

The correct option is B 30° , 60° , 90°


Let $\angle ABC=\theta$
Then, $sin\theta =\frac{1}{2}andcos\theta =\frac{\sqrt{3}}{2}$
This happens when $\theta =30°$

We know that, $\angle CAB=90°$
Then, $\angle ACB=180°-90°-30°=60°$
(Angle sum property of a triangle)

So, if the sides are in the ratio $1:\sqrt{3}:2$, then the angles are 30° , 60° , 90°.