Question

A tree casts a 25m shadow when the angle of elevation to the sun is 40. Approximately how tall is the tree?

Answer 1

Check the picture below.

make sure your calculator is in Degree mode.

Answer 2

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.

$\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}$

$\text{tan}(40^{\circ})=\frac{h}{25}$

$\frac{h}{25}=\text{tan}(40^{\circ})$

$\frac{h}{25}\cdot 25=\text{tan}(40^{\circ})\cdot 25$

$h=(0.839099631177)\cdot 25$

$h=20.977490779425$

$h\approx 20.98$

Therefore, the tree is approximately 20.98 meters tall.