Question

Construct a $\Delta ABC$ in which $BC=6$ cm, $\angle A={60}^{\circ }$ and altitude through $A$ is $4.5$ cm. Write the steps of construction.

Answer 1

Steps of Construction :
1. Draw a line segment $BC=6$ cm and make an $\angle CBP={60}^{\circ }$ downwards.
2. Draw perpendicular bisector $RQ$ of $BC$ and perpendicular $EB$ to $BP$. Let they intersect each other at $O$. Let $M$ be the mid-point of $BC$.
3. With $O$ as centre and radius $=OB$, draw a circle
4. Mark a point $L$ on $RQ$ such that $LM=4.5$ cm
5. Draw a line m parallel to $BC$ through $L$ intersecting the circle in two points say $A$ and $A^{\prime }$.
6. Join $AB,AC$ and $A^{\prime }B,A^{\prime }C$.
Either of these $\Delta s$ $ABC$ or $A^{\prime }BC$ is the required triangle.