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 7 cm. At point B, draw an angle of ${75}^{\circ }$, say $\angle XBC={75}^{\circ }$.
Step 2: With compass needle at point B, cut a line segment BD=13 cm (that is equal to AB + AC) on the ray BX.
Step 3: Join DC.
Step 4: Draw Perpendicular bisector MN of CD intersecting BD.
Step 4: The point at which MN intersect BD is the required point A, and hence $\Delta ABC$ is the required triangle.