Question

GEOMETRY! The diagram shows 5 ft student standing near a tree. The shadow of the student and the shadow of the tree end at point A. What is the height of the tree? Show all your work, and make sure to include units in your final answer.

Answer 1

Answer: 24.99 ft

Step-by-step explanation:

1. You can find the angle A as following:

$A=arctan(\frac{5}{8})\\A=32\°$

2. Now, you can calculate the height of the tree as following:

$tan(A)=\frac{opposite}{adjacent}$

Where:

A=32°

opposite=x

adjacent=40

3. When you substitute values and solve for x, you obtain that the height of the tree in feet is:

$tan(A)=\frac{x}{40}\\x=40*tan(32\°)\\x=24.99$