Pythagorean Theorem Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
A right triangle has a hypotenuse of 1313 and one leg of length 55. Find the other leg.

Solution

  1. 1
    Apply a2+b2=c2a^2 + b^2 = c^2 with c=13c = 13 and a=5a = 5: 52+b2=1325^2 + b^2 = 13^2.
  2. 2
    Simplify: 25+b2=16925 + b^2 = 169, so b2=169−25=144b^2 = 169 - 25 = 144.
  3. 3
    Take the square root: b=144=12b = \sqrt{144} = 12.

Answer

b=12b = 12
When you know the hypotenuse and one leg, rearrange the theorem to solve for the missing leg. The 55-1212-1313 combination is another well-known Pythagorean triple.

About Pythagorean Theorem

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

Learn more about Pythagorean Theorem →

More Pythagorean Theorem Examples

Example 1 easy

A right triangle has legs of length [formula] and [formula]. Find the hypotenuse.

Example 3 hard

A ladder [formula] m long leans against a wall. The foot of the ladder is [formula] m from the base

Example 4 hard

A right triangle has legs of length [formula] and [formula], and hypotenuse [formula]. Find [formula

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