The length of the hypotenuse of a right triangle is 17 centimeters and the length of one of the legs is 8 centimeters. What is the number of centimeters in the length of the second leg?

1 Answer
sente
Dec 1, 2015

Use the Pythagorean theorem to find the length to be
#15"cm"#

Explanation:

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of its legs. That is, in a right triangle with legs #a# and #b# and hypotenuse #c#

#a^2 + b^2 = c^2#

In this particular triangle, we have #a = 8"cm"# and #c = 17"cm"# and we need to solve for #b#. Applying the theorem,

#(8"cm")^2 + b^2 = (17"cm")^2#

#=> b = (17"cm")^2 - (8"cm")^2 = 289"cm"^2 - 64"cm"^2 = 225"cm"^2#

#=> b = sqrt(225"cm"^2) = 15"cm"#

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