A person is standing 40 m away from a building. If the angle of elevation to the top of the building is 60 degrees, what is the height of the building?
Practice Questions
1 question
Q1
A person is standing 40 m away from a building. If the angle of elevation to the top of the building is 60 degrees, what is the height of the building?
20√3 m
40 m
30 m
50 m
Using tan(60°) = height/40, we have √3 = height/40. Therefore, height = 40√3 m.
Questions & Step-by-step Solutions
1 item
Q
Q: A person is standing 40 m away from a building. If the angle of elevation to the top of the building is 60 degrees, what is the height of the building?
Solution: Using tan(60°) = height/40, we have √3 = height/40. Therefore, height = 40√3 m.
Steps: 7
Step 1: Understand the problem. A person is standing 40 meters away from a building and looking up at the top of the building at an angle of 60 degrees.
Step 2: Visualize the situation. Imagine a right triangle where one side is the height of the building, the other side is the distance from the person to the building (40 m), and the angle between the ground and the line of sight to the top of the building is 60 degrees.
Step 3: Use 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 person to the building). So, tan(60°) = height / 40.
Step 4: Find the value of tan(60°). The value of tan(60°) is √3.
Step 5: Set up the equation. Now we have √3 = height / 40.
Step 6: Solve for height. Multiply both sides of the equation by 40 to isolate height: height = 40 * √3.
Step 7: Calculate the height. The height of the building is 40√3 meters.
