Building Height Calculation using Trigonometry

Question:

From the given data, how can we determine the height of the building with the 136-foot antenna using trigonometric concepts?

Answer:

To find the height of the building, we can utilize trigonometric concepts and set up an equation based on the angles of elevation provided. By solving this equation, we can determine the height of the building.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. In this scenario, we are given the angles of elevation to the top and bottom of the 136-foot antenna on top of the building. By using trigonometric ratios, we can set up an equation to calculate the height of the building.

Let's denote the height of the building as 'h'. From the information given, we can establish the following equation:

h / tan(28.5°) - h / tan(21.5°) = 136

By solving for 'h' in the equation above, we can determine that the height of the building is approximately 415 feet. Therefore, the correct answer to the question is option d) 415 feet.

Trigonometry plays a crucial role in solving real-world problems like calculating building heights, distances, and angles. It is a powerful tool that finds applications in various fields such as engineering, physics, and astronomy.