Construct ΔABC, given m∠A = 60°, m∠B = 30° and AB = 5.8 cm.
A rough sketch of the required ΔABC is as follows.
The steps of construction are as follows.
1) Draw a line segment AB of length 5.8 cm.
2) At point A, draw a ray AX making 60º angle with AB.
3)At point B, draw a ray BY, making 30º angle with AB.
4) Point C has to lie on both the rays, AX and BY. Therefore, C is the point of intersection of these two rays.
This is the required triangle ABC.