Question

Jill is standing at the base of her apartment building. She measures the angle of elevation to the top of a nearby tower to be 40º. Then Jill goes to the roof of her apartment building, directly above her previous position, and measures the angle of elevation to the top of the same tower to be 30°. If the height of the tower is 100 meters, the height of Jill's apartment building is meters.

Answer 1

Answer:

1) From the measure of 40°, you can write:

tan(40°) = 100/x, where x is the base from the building to the tower

⇒x=100/tan(40°) = 119,18 m

2) From the measure of 30°, you can write

tan(30°) = y / 119,18, where y is the height from the roof of Jill's building to the top of the tower.

Then, y = tan(30°) * 119,18 = 68,81 m

3) The height of Jill's building is 100 - 68,81 = 31,19 m

Answer 2

When the height of the tower is 100 meters, the height of Jill's apartment building is 31.19m

How to calculate the height?

Let the base from the building to the Rowe be represented by x. Based on the information given, the value will be:

x = 100/tan 40°

x = 119.18m

The height can be represented as:

= 100 - [tan30° × 119.18]

= 100 - 68.81

= 31.19m

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