Question

Construct a triangle ABC in which $BC=7cm,\angle B={75}^{\circ }andAB+AC=13cm$

Answer 1

Steps to construct the required triangle are as follows:

Step 1: Draw a line segment BC of length 7 cm.
Step 2: At point B, draw an angle of ${75}^{\circ }$, say $\angle XBC={75}^{\circ }$.
Step 3: With compass needle at point B, cut a line segment BD = 13 cm (that is equal to AB + AC) on the ray BX.
Step 4: Join DC.
Step 5: Draw the perpendicular bisector of CD to intersect BD at A.

Hence, $\Delta ABC$ is the required triangle.