Question
Draw a triangle $ABC$ in which $BC = 4\ cm, AB = 3\ cm$ and $\angle\text{B}=45^\circ.$ Also, draw a perpendicular from $A$ on $BC.$
✓
Answer
Steps of construction:
Step I: Draw a line segment $AB$ of length $3\ cm.$
Step II: Draw an angle of $45^\circ $ and cut an arc at this angle at a radius of $4\ cm$ at $C.$
Step III: Join $AC$ to get the required triangle.
Step IV: With $A$ as centre, draw intersecting arcs at $M$ and $N.$
Step V: With centre $M$ and radius more than half of $MN$, cut an arc on the opposite side of $A.$
Step VI: With $N$ as centre and radius the same as in the previous step, cut an arc intersecting the previous arc at $E.$
Step VII: Join $AE$, it meets $BC$ at $D$, then $AE$ is the required perpendicular.
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