Draw a triangle ABC in which BC = 4 cm, AB = 3 cm and ∠B = 45°. Also, draw a perpendicular from A on BC.

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Solution

Steps of construction:

Draw a line segment AB of length 3 cm.

Draw an angle of 45 $°$ and cut an arc at this angle at a radius of 4 cm at C.

Join AC to get the required triangle.

With A as centre, draw intersecting arcs at M and N.

With centre M and radius more that $\frac{1}{2} M N$ , cut an arc on the opposite side of A.

With N as centre and radius the same as in the previous step, cut an arc intersecting the previous arc at E.

Join AE, it meets BC at D, then AE is the required perpendicular.

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