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A right triangle has one leg that is 7 meters long. The hypotenuse is 25 meters. Find the length of the other leg. Leave it as an exact answer.

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Answer:

The other leg is 24 meters long.

Explanation:

Since we have a right triangle and are given two side lengths, we can find the length of the other leg using the Pythagorean Theorem, which is given by:

a^2 + b^2 = c^2, where

  • a and b are the lengths of the legs,
  • and c is the length of the hypotenuse.

We can find b (the length of the other leg) by substituting 7 for a and 25 for c:

Step 1: Plug in 7 for a and 25 for c and simplify:

7^2 + b^2 = 25^2

49 + b^2 = 625

49 + b^2 = 625

Step 2: Subtract 49 from both sides:

(49 + b^2 = 625) - 49

b^2 = 576

Step 3: Take the square root of both sides to solve for b (the length of the other leg):

√b^2 = √576

b = ± 24

b = 24

Thus, the length of the other leg is 24 meters.

7, 24, and 25 are what we call a Pythagorean Triple, meaning you get an exact answer for the legs and hypotenuse when solving for either one.

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