Problem

To estimate the height of a building, two students find the angle of elevation from a point (at ground level) down the street from the building to the top of the building is $32^{\circ}$. From a point that is 200 feet closer to the building, the angle of elevation (at ground level) to the top of the building is $55^{\circ}$. If we assume that the street is level, use this information to estimate the height of the building. The height of the building is feet.

Solution

Step 1 :Define the variables h (height) and d (distance).

Step 2 :Set up two equations based on the given information. The first equation is \(h = \tan(32^{\circ}) \cdot d\), and the second equation is \(h = \tan(55^{\circ}) \cdot (d - 200)\).

Step 3 :Solve the system of equations. The solution is \(d \approx 355.58\) and \(h \approx 222.19\).

Step 4 :The solution to the system of equations gives the height of the building as approximately 222.19 feet.

Step 5 :Final Answer: The height of the building is approximately \(\boxed{222.19}\) feet.

From Solvely APP
Source: https://solvelyapp.com/problems/PWVj8B4lBe/

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