The answer is:
The height of the building is 94.29 feet.
<h2>Why?</h2>To solve the problem, we need to consider that two triangles are formed depending on the distance where the surveyor is standing.
We have a first triangle which its base will be called "x" and its height will be called "h" with an angle of elevation from a point on the ground, equal to 31°.
Also, we have a second triangle which base is equal to "x" + 57.1 feet, and a height "h", with an angle of elevation from a point on the ground, equal to 23.8°
We need to use a trigonometric identity that establishes a relationship between the height and the base. So, using the tangent trigonometric identity, we have:
For the first triangle:
For the second triangle:
Then, making both equation equals, in order to find "x", we have:
Then, we substituting "x" into any of the equations, we have:
Substituting into the first equation:
Hence, the height of the building is 94.29 feet.
Have a nice day!