Question

The angle of elevation to the top of a 10-story skyscraper is measured to be 3from a point on the ground 2,000 feet from the building. What is the height of the skyscraper to the nearest hundredth foot? A.285.09 feet B.104.67 feet C.66.58 feet D.104.82 feet

Answer 1

It's D, 104.82 feet.

Hope this helps,

:)

Answer 2

The correct option is D. 104.82 feet

Explanation:

For better understanding of the solution see the attached figure of the problem :

Angle of elevation, θ = 3°

Distance between building and observing point = 2000 feet

⇒ BC = 2000 feet

To find : Height of the building, AB

Since, the building and the ground surface are perpendicular to each other

⇒ ΔABC is a right angle triangle right angled at B

Now, to find height of building using property of tan in ΔABC

`\tan\theta=(Perpendicular)/(Base)\\\\\tan 3=(AB)/(2000)\\\\\implies 0.0524=(AB)/(2000)\\\\\implies AB=2000* 0.0524\\\\\implies\bf AB = 104.8\thinspace{ feet}`

Hence, The height of the building = 104.8 feet

Therefore, The correct option is D. 104.82 feet