Question

Construct a right angled triangle whose hypotenuse measure $6.5cm$ and one of its acute angle measure ${60}^o$

Answer 1

Steps to construct a right angle triangle whose hypotenuse and an angle are given:
1. Draw a line $AB=6.5cm$
$\Rightarrow AB$ is the hypotenuse.
Hence Let $\angle C={90}^{\circ }$

2. Take $B$ as a centre, draw an angle of $\angle B={60}^{\circ }$ with ruler and compass

We know that
$\angle A+\angle B+\angle C={180}^{\circ }$ [Angle sum property]
$\Rightarrow \angle A=180-{60}^{\circ }-{90}^{\circ }$
$\Rightarrow \angle A={30}^{\circ }$

4. Take $A$ as a centre, draw an angle of $\angle C={30}^{\circ }$ with ruler and compass.
5. Join the angle lines to meet each other at point $B.$

Thus $△ABC$ is the required triangle with $\angle C={90}^{\circ },AB=6.5cm$ and $\angle B={60}^{\circ }$