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find sides of right triagle when you know hypoteneuse

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see attached file. Find a, b and h. know hypotenuese is square root of 3 plus square rrot of 12

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The equation to use when dealing with sides and right triangles is known as the Pythagoras' Theorem.

This states that the sum of the square of each side (A,B) is equal to the square of the hypotenuse (C). Mathematically speaking,

A^2+B^2 = C^2

(A^2 means "A squared" and it's A*A)
(sqrt(x) is read as "square root of x")
because there are 3 right triangles in this picture, we can write Pythagoras' Theorem 3 times:

First the large triangle:

a^2+b^2 = (sqrt(3)+sqrt(12))^2 .....(1)

The triangle on the left:

(sqrt(3))^2+h^2 = b^2 .....(2)

The triangle on the right:

(sqrt(12))^2+h^2 = a^2 ...

Solution Summary

The expert finds sides of right triangles when you know the hypoteneuse.