Answer:
Explanation:
We can use trigonometry to solve this problem. Let's draw a diagram to visualize the situation:
*
/|
/ |
/ |h
/ |
/θ |
/ |
/______|\
d 58°
In this diagram, the height of the building is represented by "h", the angle of elevation of the sun is 58 degrees, and the length of the shadow is 84 feet. We also know that the angle of elevation is complementary to the angle of depression, which is the angle between the horizontal and the line from the top of the building to the end of the shadow. Therefore, we can find the angle of depression by subtracting 58 degrees from 90 degrees:
θ = 90° - 58° = 32°
Now, we can use the tangent function to relate the height of the building to the length of the shadow and the angle of depression:
tan(θ) = h / d
Solving for h, we get:
h = d * tan(θ)
Substituting the given values, we get:
h = 84 * tan(32°)
Using a calculator, we can evaluate tan(32°) to be approximately 0.6250. Substituting this value in the equation, we get:
h = 84 * 0.6250 = 52.5
Therefore, the height of the building is approximately 52.5 feet. Rounded to the nearest tenth, the answer is 52.5 feet.