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Yuki888 [10]
3 years ago
11

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?

Mathematics
1 answer:
lorasvet [3.4K]3 years ago
3 0

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.

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