Question

Joe is installing a light fixture on a wall using a 10 foot ladder. A flower garden is planted along the wall, so Joe must place his ladder 6 feet away from the wall. How high up the wall will his ladder reach?

Answer 1

The ladder is 8 feet high up on the wall.

Explanation:

Let the height up of the ladder on the wall be represented by h. The ladder leaning on the wall, wall and distance of the foot of ladder from the wall form a right angled triangle.

So, applying the Pythagoras theorem;

`/hyp/^(2)` =
`/adj 1/^(2)` +
`/adj 2/^(2)`

`/10/^(2)` =
`/6/^(2)` +
`/h/^(2)`

100 = 36 +
`h^(2)`

so that,

`h^(2)` = 100 - 36

= 64

⇒ h =
`√(64)`

= 8 feet

The ladder is 8 feet high up on the wall.