Construct an isosceles triangle whose altitude is 6.6 cm and vertex angle is 60°.

Here, we are given with altitude of triangle, that is, 6.6 cm and vertex angle equals to 60°. Let us construct an isosceles triangle using the following steps of construction.

Steps of construction:

1. Draw a line segment XY using a ruler of any length.

2. Take a point M on line XY and draw a perpendicular line MP such that MP ⊥ XY; use protractor to measure the angle 90°.

3. Now, with M as centre draw an arc of radius 6.6 cm cutting MP at A, using a protractor and a ruler.

4. Construct B and C on XY such that, ∠MAB = 30° and ∠MAC = 30° . Measure the angles using a protractor.

Thus, ABC is required triangle.