Question

Construct a $△ABC$ in which the base $BC=5$ cm, $\angle BAC={40}^{\circ }$ and the median from $A$ to $BC$ is $6$ cm. Also measure the length of the altitude from $A$.

Answer 1

$1$. Draw a line segment $BC=5$ cm
$2$. Draw $BX$ such that $\angle CBX={40}^{\circ }$
$3$. Draw $BY\perp BX$.
$4$. Draw the perpendicular bisector of $BC$ intersecting $BY$ at $O$ and $BC$ at $M$.
$5$. With $O$ as centre and $OB$ as radius, draw the circle.
$6$. The major arc $BKC$ of the circle, contains the vertical angle ${40}^{\circ }$.
$7$. With $M$ as centre draw an arc of radius $6$ cm meeting the circle at $A$ and $A^{\prime }$.
$8$. Completer $△ABC$ on $A^{\prime }BC$ which is the required triangle.
$9$. Produce $CB$ to $CZ$.
$10$. Draw $AE\perp CZ$.
$11$. Length of the altitude $=5.1$ cm.