Question

Construct a $△PQR$ which the base $PQ=4.5cm,\angle R={35}^{\circ }$ and the median from $R$ to $RG$ is $6cm$.

Answer 1

Construction:
Step (1) Draw a line segment $PQ=4.5cm$
Step (2) At $P$, draw PE such that $\angle QPE={35}^{\circ }$.
Step (3) At $P$, draw PF such that $\angle EPF={90}^{\circ }$.
Step (4) Draw ${\perp }^{┌}$bisector to $PQ$ which intersects $PF$ at $O$.
Step (5) With O centre OP as raidus draw a circle.
Step (6) From G mark arcs of $6cm$ on the circle.
Mark them as R and S.
Step (7) Join PR and RQ.
Step (8) PQR is the required triangle.