To find the height of the tree, we can use the tangent of the angle of elevation. The angle of elevation to the top of the tree is 45°, and the tangent of 45° is 1.
The formula for the tangent of an angle in a right triangle is:
\[ \tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}} \]
In this case:
- The "opposite" side is the height of the tree (which we need to find).
- The "adjacent" side is the length of the shadow, which is 20 meters.
Setting up the equation with the tangent of 45°:
\[ \tan(45°) = \frac{\text{height of tree}}{20} \]
Since \(\tan(45°) = 1\):
\[ 1 = \frac{\text{height of tree}}{20} \]
This simplifies to:
\[ \text{height of tree} = 20 \text{ meters} \]
Therefore, the height of the tree is 20 meters.
1 answer