Pythagorean Theorem Math Example 1

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Example 1

easy
A right triangle has legs of length 33 and 44. Find the hypotenuse.

Solution

  1. 1
    Apply the Pythagorean theorem: a2+b2=c2a^2 + b^2 = c^2.
  2. 2
    Substitute: 32+42=c2⇒9+16=c2⇒c2=253^2 + 4^2 = c^2 \Rightarrow 9 + 16 = c^2 \Rightarrow c^2 = 25.
  3. 3
    Take the positive square root: c=25=5c = \sqrt{25} = 5.

Answer

c=5c = 5
The Pythagorean theorem relates the three sides of a right triangle. The hypotenuse (opposite the right angle) is always the longest side. The 33-44-55 triple is the most common 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 2 medium

A right triangle has a hypotenuse of [formula] and one leg of length [formula]. Find the other leg.

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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