A person standing 40 meters away from a building observes the top of the building at an angle of elevation of 45 degrees. What is the height of the building?
Practice Questions
1 question
Q1
A person standing 40 meters away from a building observes the top of the building at an angle of elevation of 45 degrees. What is the height of the building?
20 m
40 m
30 m
10 m
Height = distance * tan(angle) = 40 * 1 = 40 m.
Questions & Step-by-step Solutions
1 item
Q
Q: A person standing 40 meters away from a building observes the top of the building at an angle of elevation of 45 degrees. What is the height of the building?
Step 1: Understand the situation. A person is standing 40 meters away from a building.
Step 2: The person looks up at the top of the building and sees it at an angle of elevation of 45 degrees.
Step 3: Recall that the angle of elevation is the angle between the horizontal line (where the person is standing) and the line of sight to the top of the building.
Step 4: Use the tangent function from trigonometry. The formula is: Height = distance * tan(angle).
Step 5: Plug in the values. The distance is 40 meters and the angle is 45 degrees.
Step 6: Calculate tan(45 degrees). The value of tan(45 degrees) is 1.
Step 7: Multiply the distance by the tangent value: Height = 40 meters * 1.
Step 8: The result is 40 meters. Therefore, the height of the building is 40 meters.
