From a point A, the angle of elevation of the top of a building is 45 degrees. If the height of the building is 20 meters, how far is point A from the base of the building?
Practice Questions
1 question
Q1
From a point A, the angle of elevation of the top of a building is 45 degrees. If the height of the building is 20 meters, how far is point A from the base of the building?
10 m
20 m
30 m
40 m
Using tan(45°) = height/distance, we have 1 = 20/distance. Therefore, distance = 20 m.
Questions & Step-by-step Solutions
1 item
Q
Q: From a point A, the angle of elevation of the top of a building is 45 degrees. If the height of the building is 20 meters, how far is point A from the base of the building?
Solution: Using tan(45°) = height/distance, we have 1 = 20/distance. Therefore, distance = 20 m.
Steps: 10
Step 1: Understand that the angle of elevation is the angle formed between the horizontal line from point A and the line of sight to the top of the building.
Step 2: Note that the angle of elevation is 45 degrees.
Step 3: Recall that the height of the building is 20 meters.
Step 4: Use the tangent function, which relates the angle of elevation to the height of the building and the distance from point A to the base of the building.
Step 5: Write the formula: tan(angle) = height / distance.
Step 6: Substitute the known values into the formula: tan(45°) = 20 / distance.
Step 7: Know that tan(45°) equals 1.
Step 8: Set up the equation: 1 = 20 / distance.
Step 9: Rearrange the equation to find distance: distance = 20 / 1.
Step 10: Calculate the distance: distance = 20 meters.
