Question

Construct an isosceles triangle whose altitude is $6.6cm$ and vertex angle is ${60}^{\circ }$

Answer 1

Steps of construction:

Draw a line segment $XY$

Take a point $M$ on $XY$ and draw a line $MP\perp XY$

With $M$ as centre and radius $6.6cm$, draw an arc cutting $MP$ at $A$.

Construct $B$ and $C$ on $XY$ such that $\angle MAB=\frac{60˚}{2}=30˚$ and $\angle MAC=\frac{60˚}{2}=30˚$

Then $△ABC$ is the required triangle.