Question

Using ruler and compasses only, construct a $△$ABC, from the following data :

AB + BC + CA = 12 cm, $\angle B={45}^{\circ }and\angle C={60}^{\circ }$.

Answer 1

Steps of construction :

(i) Draw a line segment PQ = 12 cm.

(ii) Draw a ray PX at P making are angle of ${45}^{\circ }$ and at Q, QY making an angle of ${60}^{\circ }$.

(iii) Draw the angle bisectors of $\angle Pand\angle Q$ meeting each other at A.

(iv) Draw the perpendicular bisector of AP and AQ intersecting PQ at B and C respectively.

(v) Join AB and AC.

$△$ABC is the required triangle.