Question

The angle of elevation to the top of a skyscraper is measured to be 2 degrees from a point on the ground 1 mile from the building. How tall is the skyscraper?

Answer 1

0.034921 miles or 1843774 feet tall

Explanation:

Using trigonometric functions we know that
`x=rcos(\theta)` and
`y=rsin(\theta)` where
`\theta`=angle and r is the hypotenuse of the triangle.

First we will calculate the hypotenuse using the x equation, since we know x = 1 mile (distance from the building on the ground) we have:

`x=rcos(\theta)\\\\1=rcos(2)\\\\r=(1)/(cos(2)) \approx. 1.0061mi`

Now we will calculate the height of the building using the y equation and so:

`y=rsin(\theta)\\\\y=(1)/(cos(2)) * sin(2) = (sin(2))/(cos(2))=tan(2)=0.034921mi`

The building is 0.034921 miles or approximately 184.3774 feet tall.