Question

The base of a 40 foot ladder is 8 feet from the wall how high is the ladder on the wall

Answer 1

Therefore, height of the wall at which the ladder is placed is AB = 39.12 foot.

Explanation:

Let,

AB = height of the wall at which the ladder is placed

AC = height of the ladder = 40 foot

BC = distance from the wall to the base of the ladder = 8 feet

To Find:

AB = height of the wall at which the ladder is placed = ?

Solution:

Consider a right angled triangle Δ ABC right angle at angle B,

So by Pythagoras theorem we have

`(\textrm{Hypotenuse})^(2) = (\textrm{Shorter leg})^(2)+(\textrm{Longer leg})^(2)`

AC² = AB² + BC²

Substituting the given values in above equation we get

40² = AB² + 8²

∴ AB² = 40² - 8²

∴ AB² = 1536

`\therefore AB =\pm√(1536) \\\\(distance\cannot\ be\ negative)\\\therefore AB =39.19\ foot\\`

Therefore, height of the wall at which the ladder is placed is AB = 39.12 foot.