If in a right angle triangle the lengths of the two sides
including the right angle are 27 and 120 units long,
how many units is the third side?
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We can use the Pythagorean theorem to find the length of the third side of the right triangle.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, we are given the lengths of the two sides including the right angle, which are 27 and 120 units long.
So, we can calculate the length of the hypotenuse as:
hypotenuse^2 = 27^2 + 120^2
hypotenuse^2 = 729 + 14400
hypotenuse^2 = 15129
hypotenuse = sqrt(15129)
hypotenuse = 123
Therefore, the length of the third side is 123 units.