Question

from the window of one building, Uncle G finds the angle of elevation of the top of a second building is 41° and the angle of depression of the bottom is 54°. The buildings are 56.0m apart. Determine the height of the second building

Answer 1

Given:

The angle of elevation of the top of second building is 41 degree.

The angle of depression of the bottom is 54 degree.

Angle G is at point A.

To find the distance of DC that means the height of the second building.

As angle EAC is 54 degree it implies the angle ACB is also 54 degree

( alternate angle)

Use the tan ratio,

`\begin{gathered} \tan (54^(\circ))=(AB)/(BC) \\ 1.3764=(AB)/(56) \\ AB=77.0784 \end{gathered}`

It implies side CE = 77.0784 m

Now, consider traingle ADE,

`\begin{gathered} \tan (41^(\circ))=(DE)/(AE) \\ 0.8693=(DE)/(56) \\ DE=48.6808\text{ m} \end{gathered}`

So, the height of the second building is,

`\begin{gathered} DC=DE+EC \\ =48.6808+77.0784 \\ =125.7592 \\ \approx125.76 \end{gathered}`

Answer: the height of the second building is 125.76 m