Question

Construct an isosceles triangle whose altitude is $4cm$ and vertex angle is ${80}^{\circ }$

Answer 1

Steps of construction
$1$. Draw a line segment $XY$.
$2$. Take a point $M$ on $XY$ and draw a line $MP\perp XY$.
$3$. With $M$ as centre and radius $4cm$, draw an arc cutting $MP$ at $A$.
$4$. Construct $B$ and $C$ on $XY$ such that $\angle MAB={80}^{\circ }/2={40}^{\circ }$ and $\angle MAC={80}^{\circ }/2={40}^{\circ }$.
Then $ABC$ is the required triangle.