Answer:
Approximately 20.98 meters tall.
Step-by-step explanation:
We have been that a tree casts a 25 m shadow when the angle of elevation to the sun is 40 degrees. We are asked to find the height of the tree.
First of all, we will draw a graph to represent the given scenario.
The shadow of tree will form a right triangle with respect to tree and angle of elevation with ground as shown in the image.
We know that tangent relates opposite side of a right triangle with adjacent.
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
[tex]\text{tan}(40^{\circ})=\frac{h}{25}[/tex]
[tex]\frac{h}{25}=\text{tan}(40^{\circ})[/tex]
[tex]\frac{h}{25}\cdot 25=\text{tan}(40^{\circ})\cdot 25[/tex]
[tex]h=(0.839099631177)\cdot 25[/tex]
[tex]h=20.977490779425[/tex]
[tex]h\approx 20.98[/tex]
Therefore, the tree is approximately 20.98 meters tall.
