Geometry

How do you find the altitudes of a right triangle with the three sides?

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  1. If you just want the area, use Hero's formula:
    Let
    p = (a+b+c)/2 = half-perimeter
    Area = √(p(p-a)(p-b)(p-c))

    If it's really the altitude you need, then find each angle using the cosine law:
    cos(A)=(b²+c²-a²)/(2bc)
    where a,b,c are lengths of sides opposite to the respective angles A, B and C. Altitudes are AD, BE, CF.
    Altitude CF can be found by b*sin(A), etc.

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