Question

Gabe is sitting in his boat and sees a famous building onshore which is known to be 250 meters tall. gabe sights the top of the building, and finds that the angle of elevation is 19°. about how far, in meters, is gabe from the base of the building? (disregard gabe's height from the water in your calculations.)

Answer 1

The distance between the gabe and the base of the building is 726.07 meters.

Step-by-step explanation:

It is given that,

Gabe is sitting in his boat and sees a famous building onshore which is known to be 250 meters tall.

The angle of elevation, θ = 19°

We have to find the the distance between the gabe and the base of the building. From the attached figure, AB = height of building = 250 meters

BC = distance between the gabe and the base of the building

Using trigonometric equation as :

`tan\ \theta=(AB)/(BC)`

`BC=(AB)/(tan\ \theta)`

`BC=(250)/(tan(19))`

BC = 726.05 meters

So, the gabe is 726.05 meters away from the base of the building.

Answer 2

If we connect Gabe's current position to the top of the building, to the bottom of the building and back to Gabe, we form a right triangle with the height of 250 m and the angle opposite to the height being equal to 19°. If we let x be his distance from the building, we use the trigonometric formula,
tan 19° = x/250 m
The value of x from the equation is 86.08 m. Thus, the answer is 86.08 m.