Question

A straight ladder 16 metres long is placedagainst a vertical wall with its lower end4 m away from the wall. How high up thewall does it reach? Give your answer cor-/rect to the nearest tenth of a metre.

Answer 1

We are given a ladder that is 16 meters long is placed against a wall. We have the following diagram:

To determine the value of the height "h" we can use the Pythagorean theorem since the ladder and the wall form a right triangle.

`16^2=h^2+4^2`

Solving the squares:

`256=h^2+16`

Now, we subtract 16 from both sides:

`\begin{gathered} 256-16=h^2+16-16 \\ 240=h^2 \end{gathered}`

Now, we take the square root to both sides:

`\begin{gathered} √(240)=h \\ 15.5=h \end{gathered}`

Therefore, the height is 15.5 meters.