In a right-angled triangle ABC, the angle is C = 90 °; AC = 6cm; AB = 9cm, CD is height. Find BD.

In a right-angled triangle ABC, we can write and find the cosine of the angle A:
Cos A = AC / AB = 6/9 = 2/3.
Now consider a right-angled triangle ACD, in which the hypotenuse AC = 6 cm (by condition) and cos A = 2/3 are known.

Using the cosine, we find the leg AD adjacent to the corner A:
AD = cos A * AC = 2/3 * 6 = 4 cm.
Find BD:
BD = AB – AD = 9 – 4 = 5 cm.
Answer: BD = 5 cm.