Question

A 15 foot pole is leaning against a tree. The bottom of the pole is 8 feet away from the bottom of the tree. Approximately how high up the tree does the top of the pole reach?

Answer 1

Technically, its 12 feet, but 13 feet is also a good answer. 12 is the right answer, though, cause i got a 100 on the thing that the question was on, and the answer I chose was 13, sooo...

Answer 2

The top of the pole is approximately 13 feet high up the tree.

Explanation:

The diagram for the given scenario is shown below.

From triangle ABC, A is the top of pole and B is the bottom of pole.

AC is the height of tree. BC is the distance of the bottom of pole from the tree.

Given:

AB = 15 ft, BC = 8 ft

To find:

AC = ?

Since triangle ABC is right angled triangle, we apply Pythagoras Theorem to find the unknown side. So,

`AC^2+BC^2=AB^2\\\\AC^2+8^2=15^2\\\\AC^2+64=225\\\\AC^2=225-64\\\\AC^2=161\\\\AC=√(161)=12.7\approx 13\ ft`

Therefore, the height of the tree is approximately 13 ft.