Question

From the given diagram,ABC is a Right angled triangle ,right angled at C. Find the height h, the height is drawn to the hypotenuse?​

Answer 1

Let the point of intersection of h and AB be P.

In triangle CPB,

h^2 + 18^2 = BC^2 ... (a)

In triangle ACP, h^2 + 50^2 = AC^2 ... (b)

In triangle ABC,

AB^2 = AC^2 + BC^2

Using a and b

68^2 = h^2 + 50^2 + h^2 + 18^2

4624 = 2h^2 + 2500 + 324

2h^2 = 4624 - 2824 = 1800

h^2 = 900

h = 30 units