Pythagorean Theorem Math Example 3

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Example 3

hard
A ladder 1010 m long leans against a wall. The foot of the ladder is 66 m from the base of the wall. How high up the wall does the ladder reach?

Solution

  1. 1
    Model as a right triangle: hypotenuse =10= 10 m (ladder), base =6= 6 m (ground distance), height =h= h (wall).
  2. 2
    Apply the Pythagorean theorem: 62+h2=102⇒36+h2=1006^2 + h^2 = 10^2 \Rightarrow 36 + h^2 = 100.
  3. 3
    Solve: h2=64h^2 = 64, so h=8h = 8 m.

Answer

h=8 mh = 8 \text{ m}
Real-world problems involving right angles often reduce to the Pythagorean theorem. Identifying which measurement is the hypotenuse is the key first step.

About Pythagorean Theorem

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

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More Pythagorean Theorem Examples

Example 1 easy

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

Example 2 medium

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

Example 4 hard

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

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