A building is 40 m high. From a point on the ground, the angle of elevation to the top of the building is 60 degrees. What is the distance from the point to the base of the building?
Practice Questions
1 question
Q1
A building is 40 m high. From a point on the ground, the angle of elevation to the top of the building is 60 degrees. What is the distance from the point to the base of the building?
20√3 m
40 m
30 m
10√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 building is 40 m high. From a point on the ground, the angle of elevation to the top of the building is 60 degrees. What is the distance from the point to the base of 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. We have a building that is 40 meters high.
Step 2: Identify the angle of elevation from the ground to the top of the building, which is 60 degrees.
Step 3: Recall the relationship in a right triangle: tan(angle) = opposite side / adjacent side.
Step 4: In our case, the opposite side is the height of the building (40 m) and the adjacent side is the distance from the point to the base of the building.
Step 5: Write the equation using the tangent function: tan(60°) = height / distance.
Step 6: Substitute the known values into the equation: tan(60°) = 40 / distance.
Step 7: Rearrange the equation to solve for distance: distance = height / tan(60°).
Step 8: Calculate tan(60°), which is √3.
Step 9: Substitute tan(60°) into the equation: distance = 40 / √3.
