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 45degrees. How tall is the tree?

Answer 1

To find the height of the tree, we can use some basic trigonometry. We know the length of the shadow and the angle of elevation from the end of the shadow to the top of the tree.

Let's denote:
- \( h \) as the height of the tree,
- \( d \) as the length of the shadow (20 meters),
- \( \theta \) as the angle of elevation (45 degrees).

Using the tangent function, we can relate these quantities:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{d}
\]

Since the angle \( \theta \) is 45 degrees, we have:

\[
\tan(45^\circ) = 1
\]

Thus, the equation becomes:

\[
1 = \frac{h}{20}
\]

Now, we can solve for \( h \):

\[
h = 20 \times 1 = 20 \text{ meters}
\]

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