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:
[tex]\begin{gathered} \tan\theta=\frac{\text{ Perpendicular}}{\text{ Base}} \\ \\ \tan52=\frac{H}{x} \\ \\ 1.2799=\frac{H}{x} \\ \\ x=\frac{H}{1.2799} \end{gathered}[/tex]For the triangle ABD is:
Perpendicular = Height
Base = x+400
Angle = 32
[tex]\begin{gathered} \tan\theta=\frac{\text{ Perpendicular}}{\text{ Base}} \\ \\ \tan32=\frac{H}{x+400} \\ \\ 0.6249=\frac{H}{x+400} \\ \\ \end{gathered}[/tex]Put the value of "x" is:
[tex]\begin{gathered} 0.6249(x+400)=H \\ \\ 0.6249x+249.947=H \\ \\ 0.6249(\frac{H}{1.2799})+249.947=H \\ \\ 0.488H+249.947=H \\ \\ 0.512H=249.947 \\ \\ H=488.407 \\ \end{gathered}[/tex]So the height of the building is: 488.407 feet
