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A right triangle has one leg of length 5 and a hypotenuse of length 16. What is the length of the other leg of the triangle?
Draw a picture to help us visualize:
We need to find a, the length of the remaining leg. Time's a-wastin', so shake a leg.
The Pythagorean Theorem tells us that a2 + 52 = 162, or a2 + 25 = 256.
Then a2 = 231, so .
Since a is a length, the final answer is .
A right triangle has a hypotenuse of 30 inches. Both of its legs are the same length. How long is a leg of this right triangle?
This problem is describing a triangle that looks like this:
We know that if we sum the squares of the legs, we find the square of the hypotenuse. We said that earlier, in that sentence you reread 37 times. Therefore:
x2 + x2 = 302
2x2 = 900
From this point onward, it's kid's stuff. We divide each side by 2 to find x2 = 450:
Since we're talking about a triangle here, we can't have a side with a negative length. As screwy as our system of measurement is compared to the metric system, at least there's no such thing as negative inches, even if a British person (hi, guys!) tries to imply that there is.
We determine that a leg of this triangle must have length .