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.

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Uniteasy Admin · Accepted Answer

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 
 
$$ 	herefore h=\dfrac{ab}{c} $$
$$ =\dfrac{11×60}{61} \approx 10.8 $$

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