A man is standing on the ground and looking at the top of a 40 m high building. If the angle of elevation is 60 degrees, how far is he from the building?
Practice Questions
1 question
Q1
A man is standing on the ground and looking at the top of a 40 m high building. If the angle of elevation is 60 degrees, how far is he from the building?
20 m
40 m
20√3 m
40√3 m
Using tan(60°) = height/distance, we have distance = height/tan(60°) = 40/√3 = 20√3 m.
Questions & Step-by-step Solutions
1 item
Q
Q: A man is standing on the ground and looking at the top of a 40 m high building. If the angle of elevation is 60 degrees, how far is he from the building?
Solution: Using tan(60°) = height/distance, we have distance = height/tan(60°) = 40/√3 = 20√3 m.
Steps: 11
Step 1: Understand the problem. A man is looking at the top of a 40 m high building from the ground.
Step 2: Identify the angle of elevation. The angle of elevation from the man to the top of the building is 60 degrees.
Step 3: Recall the relationship in a right triangle. The tangent of an angle in a right triangle is the opposite side (height of the building) divided by the adjacent side (distance from the building).
Step 4: Write the formula for tangent. tan(60°) = height / distance.
Step 5: Substitute the known values into the formula. tan(60°) = 40 m / distance.
