#### Question

A right triangle has the length of one leg 11 cm and length of the hypotenuse 61 cm. Calculate the height of the triangle on the side of the hypotenuse.

A right triangle has two adjacent sides to the right angle perpendicular to each other.

Given the length of the hypotenuse c and one of the perpendicular sides a,

Let b be the length of the 3rd side, which can be determined by Pythagorean Theorem.

b = \sqrt{c^2-a^2} =\sqrt{61^2-11^2} = 60

Using the formula for area of a triangle , we get the following equation.

A = \dfrac{1}{2}ab = \dfrac{1}{2}ch

in which A is the area of the triangle and h is the height on the side of the hypotenuse

\therefore h=\dfrac{ab}{c}

=\dfrac{11×60}{61} \approx 10.8