Given:
From the roof of a building, the angles of depression of the top and the bottom of a utility pole are 33 degrees and 52 degrees.
To find:
Find the height of the building if the pole is 27 m high.
Solution:
Let the height of the building be x m. So, the figure for the given question is as follows:
From the figure, it is clear that:
[tex]\begin{gathered} \tan52=\frac{x}{y} \\ 1.28=\frac{x}{y} \\ y=\frac{x}{1.28} \end{gathered}[/tex]
And from the second triangle:
[tex]\begin{gathered} \tan33=\frac{x-27}{y} \\ 0.65=\frac{x-27}{\frac{x}{1.28}} \\ 0.65(\frac{x}{1.28})=x-27 \\ 0.65x=1.28x-34.56 \\ -0.63x=-34.56 \\ x=\frac{-34.56}{-0.63} \\ x=54.86 \end{gathered}[/tex]
Thus, the height of the building is 54.86 m.
