A man is standing on the ground and observes the top of a building at an angle o
Practice Questions
Q1
A man is standing on the ground and observes the top of a building at an angle of elevation of 60 degrees. If he is 50 m away from the building, what is the height of the building?
25 m
43.3 m
50 m
86.6 m
Questions & Step-by-Step Solutions
A man is standing on the ground and observes the top of a building at an angle of elevation of 60 degrees. If he is 50 m away from the building, what is the height of the building?
Step 1: Understand the problem. A man is looking at the top of a building from a distance of 50 meters.
Step 2: Identify the angle of elevation. The angle at which he looks up to see the top of the building is 60 degrees.
Step 3: Recall the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the building) divided by the adjacent side (distance from the building).
Step 4: Set up the equation using the tangent function. We have tan(60°) = height / 50.
Step 5: Find the value of tan(60°). The value of tan(60°) is √3.
Step 6: Substitute the value into the equation. Now we have √3 = height / 50.
Step 7: Solve for the height. Multiply both sides by 50 to get height = 50√3.
Step 8: Calculate the height. Using a calculator, 50√3 is approximately 86.6 meters.
Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the building and the distance from it.
Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the observer, the top of the building, and the base of the building.
