Question

Construct a triangle $ABC$ in which $BC=7$ cm, $\angle A={60}^{\circ }$ and altitude through $A$ is $3.7$ cm. How many such triangles are possible? Write the steps of construction.

Answer 1

Steps of Construction :
1 Draw a line segment $BC=7$ cm
2 Construct $\angle CBX={60}^{\circ }$
3 Draw $OB\perp BX$ intersecting the perpendicular bisector of $BC$ at $O$.
4 With $O$ as centre and radius $OB$ or $OC$ draw a circle.
5 Cut $DN=3.7$ cm
6 Through $N$ draw $\perp$ on $DN$ intersecting the circle at the point $A$ and $A^{\prime }$.
7 Join $AB,AC$ and $A^{\prime }B,A^{\prime }C$

8 $\therefore \Delta ABC$ and $\Delta A^{\prime }BC$ are the required triangles
Hence, the number of possible triangles $=2$.