Question

Construct a $△ABC$ such that $AB=6$ cm, $\angle C={40}^o$ and the altitude from $C$ to $AB$ is of length $4.2$cm.

Answer 1

Construction:
(1) Draw a line segment $AB=6$ cm
(2) Draw $AX$ such that $\angle BAX={40}^o$
(3) Draw the perpendicular bisector of $AB$ intersections $AY$ at $O$ and $AB$ at $M$.
(5) Draw a circle with centre as $O$ and radius as $OA$.
(6) Mark a point $H$ on $OM$ such that $MH=4.2$ cm
(7) Draw $CH{C}^1$ parallel to $AB$ meeting the circle at $C$ and $C^1$.
(8) Complete the triangle $ABC$ which is required triangle.