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.

Collected in the board: Triangle

Steven Zheng posted 10 months ago


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


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

=\dfrac{11×60}{61} \approx 10.8

Steven Zheng posted 10 months ago

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