Question

To estimate the height of a building, two students find the angle of elevation from a point (at ground levedown the street from the building to the top of the building is 30°. From a point that is 400 feet closer tothe building, the angle of elevation (at ground level) to the top of the building is 52°. If we assume thatthe street is level, use this information to estimate the height of the building.The height of the building isfeet.

Answer 1

Given:

ground to building top is 30 degrees.

Distance = 400 feet

The angle of elevation at is top of the building = 52 degrees.

Find-: Height of the building.

Sol:

For the triangle ABC

Perpendicular = Height

Base = x

Angle = 52

Use trigonometric formula:

`\begin{gathered} \tan\theta=\frac{\text{ Perpendicular}}{\text{ Base}} \\ \\ \tan52=(H)/(x) \\ \\ 1.2799=(H)/(x) \\ \\ x=(H)/(1.2799) \end{gathered}`

For the triangle ABD is:

Perpendicular = Height

Base = x+400

Angle = 32

`\begin{gathered} \tan\theta=\frac{\text{ Perpendicular}}{\text{ Base}} \\ \\ \tan32=(H)/(x+400) \\ \\ 0.6249=(H)/(x+400) \\ \\ \end{gathered}`

Put the value of "x" is:

`\begin{gathered} 0.6249(x+400)=H \\ \\ 0.6249x+249.947=H \\ \\ 0.6249((H)/(1.2799))+249.947=H \\ \\ 0.488H+249.947=H \\ \\ 0.512H=249.947 \\ \\ H=488.407 \\ \end{gathered}`

So the height of the building is: 488.407 feet