Find the missing length indicated

x = 256

Step-by-step explanation:

Remark

Interesting question. Thanks for posting.

The small triangle has the height as the missing side.

Part One: Givens

a = 144

b = height = ?

c = 240

a^2 + b^2 = c^2

144^2 + b^2 = 240^2

20736 + b^2 = 57600                   Subtract 20736 from both sides

b^2 = 57600 - 20736

b^2 = 36864

√b^2 = √36864

b = 192

Solve for x

The relationship between the height (b) and 144 and x is

b^2 = 144 * x

36864 = 144x          Divide by 144

x = 256