Question

A person on the ground looks up at an angle of 28° and sees the top of a tree and the top of a building aligned. The tree is 20 m away from the person and the building is 60 m away from the person. What is the difference in heights between the building and tree?

Answer 1

Answer:

21.27 meters.

Step-by-step explanation:

Please find the attachment.

Let H and h represent height of building and tree respectively.

We have been given that a person on the ground looks up at an angle of 28° and sees the top of a tree and the top of a building aligned. The tree is 20 m away from the person and the building is 60 m away from the person.

We know that tangent relates opposite side of a right triangle with its adjacent side.

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

$\text{tan}(28^{\circ})=\frac{H}{60}$

$60\cdot \text{tan}(28^{\circ})=H$

$60\cdot 0.531709431661=H$

$H=31.90256589966\approx 31.90$

Similarly, we can find height of the tree.

$\text{tan}(28^{\circ})=\frac{h}{20}$

$20\cdot\text{tan}(28^{\circ})=h$

$20\cdot 0.531709431661=h$

$h=10.63418863322\approx 10.63$

$H-h=31.90-10.63$

$H-h=21.27$

Therefore, the difference in heights between the building and tree is 21.27 meters.