Question

Construct a triangle ABC, in which BC $=6.5$cm, $\angle A={45}^o$ and altitude AD$=5.5$cm.

Answer 1

Steps of construction:
(i) Draw a line segment BC$=6.5$cm. Draw an angle CBX$={45}^o$. Draw perpendicular bisector to BC show that it interest the previous perpendicular at point O.
(ii) Taken OB as radius and O as centre, draw a circle.
(iii) Intersect the perpendicular bisector PQ to make a point E at a distance of $5.5$cm from the point D. Draw a perpendicular line PQ at a point E such that it intersect the circle at points A and A'.
(iv) Join AB, AC, A'B and A'C.
Thus, ABC and A'BC are the required triangles.