Question

A tree casts a shadow that is 20 meters long. The angle of elevation from the end of the shadow to the top of the tree is 45°. How tall is the tree?(1 point)
Responses

25 meters
25 meters

10 meters
10 meters

20 meters
20 meters

15 meters

Answer 1

To find the height of the tree, we can use the relationship between the height of the tree, the length of the shadow, and the angle of elevation.

Here, we have:

- Length of the shadow (adjacent side): 20 meters
- Angle of elevation: 45°

Using the tangent function:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]

Substituting the values:
\[
\tan(45^\circ) = \frac{\text{height of the tree}}{20}
\]
Since \(\tan(45^\circ) = 1\), we have:
\[
1 = \frac{\text{height of the tree}}{20}
\]

This implies:
\[
\text{height of the tree} = 20 \times 1 = 20 \text{ meters}
\]

So, the height of the tree is **20 meters**.