Question

Construct a triangle ABC, in which $\angle$B = ${60}^{\circ }$ , $\angle$ C = ${45}^{\circ }$ and AB + BC+ CA = 22 cm.

Answer 1

Steps-

-Draw line segment PQ of length 22 cm. From P draw ray PL which makes angle ${60}^{\circ }$ with PQ using protractor. Similarly draw ray QM which makes angle ${45}^{\circ }$ with PQ.

-Using angle bisector construction method, draw angle bisectors for angles APQ and angle AQP. Let these 2 angle bisectors meet at A.

-Using perpendicular bisector construction method draw perpendicular bisectors DE for AP and FG for AQ respectively.

-Let the point where DE meets PQ be B and let the point where FG meets PQ be C. Join AB and AC. The required triangle is triangle ABC.