Question

A lot rests against the top of a wall. The head of a person 6' tall just such touches the ladder. The person is 9' from the wall and 6' from the foot of the ladder. Find the height of the wall.

Answer 1

When you have two triangles as given, they are similar triangles. It means that the ratio between corresponding sides is the same.

Corresponding sides are:

Side x (height of the wall) and the height of the person (6 feet)

Distance between the wall and the foot of the lader (6 feet + 9 feet= 15 feet) and distance between the person and the foot of the lader (6 feet)

Then, you have the next:

`(x)/(6ft)=(15ft)/(6ft)`

Solve for x:

`\begin{gathered} x=6ft\cdot(15ft)/(6ft) \\ \\ x=15ft \end{gathered}`Then, the height of the wall is 15 feet