Question

a 32 foot ladder is leaned against a wall. if the base of the ladder is 8 feet from the wall, how high up the wall will the ladder reach?

Answer 1

31 feet

Explanation:

Given: The length of ladder, leaned against wall= 32 foot

The base of ladder is 8 feet away from wall

Adjacent= 8 feet and Hypotenuse= 32 foot

we need to find height of wall till the ladder reach (Opposite).

We will use Pythagorean theorem;
`hypotenuse^(2) = adjacent^(2) +opposite^(2)`

⇒
`32^(2) = 8^(2) +opposite^(2)`

⇒
`1024= 64+opposite^(2)`

subtracting both side by 64

⇒
`Opposite^(2) = 1024-64= 960`

⇒
`Opposite= √(960) = 30.98` ≅ 31 ft

∴ 31 ft high up the wall.