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You are given one side of the triangle and the hypotenuse. You should also know that the sum of the square of the sides of a right triangle equals the hypotenuse squared.
If the sides of the triangle are a and b and the hypotenuse is h, the equation can be written:
a^2 + b^2 = h^2.
The problem tells us that one side, let's pick a for now, is 10 cm and the square of the hypotenuse is 221 cm. If we include these facts in the equation, we get,
10^2 + b^2 = 221, or
100 + b^2 = 221
Now, subtract 100 from either side to get
b^2 = 221 - 100 = 121
take the square root of either side to get
b = 11
b is the height of the triangle.