Math CentralQuandaries & Queries


Question from Slash

hi how can i find the height of a triangle from the hypotenuse and base. please
go into some details with some steps because it is hard to understand. thanks


I think you missed one word in this question. Since one side of the triangle is its hypotenuse the triangle must be a right triangle.


Since the angle between the base and the third side is a right angle. the length of the third side is the height of the triangle. Suppose this length is $x$ units, the length of the base is $b$ units and the length of the hypotenuse is $h$ units. Pythagoras Theorem then tells us that

\[x^2 + b^2 = h^{2}.\]


\[x = \sqrt{h^2 - b^2} \mbox{ units.}\]


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