Question

Practice 7:

Tim is standing 10 m away from a tree.
The distance of his eyes from his feet is 1.8 m.
Given that the distance from his eyes to the top of the tree is 14 m, find the height of the tree.

Answer 1

about 11.598 meters

Explanation:

For this situation, we will primarily rely on the Pythagorean theorem.
We can draw a (straight) 10-meter line between Tim and the tree in order to further understand the problem. Since Tim and the tree are both standing straight, a perceived line will be parallel to the ground. Another line can be drawn between Tim's eyes and the top of the tree. Please view the attached image for reference. Using the Pythagorean theorem (
`a^(2) +b^(2)=c^(2)`), we can substitute 10 for a and 14 for c ---> giving us
`a^(2) +10^(2)=14^(2)` or
`a^(2) =14^(2)-10^(2)`. We then subtract--->
`a^(2) =96` and square root both sides to get a, which is equal to about 9.798 meters. However, this is only the height from Tim's eye level; therefore, to it, we must add 1.8 meters.
Our final solution is: about 11.598 meters.