A person is standing 45 meters away from a building. If the angle of elevation t
Practice Questions
Q1
A person is standing 45 meters away from a building. If the angle of elevation to the top of the building is 45 degrees, what is the height of the building?
30 meters
45 meters
60 meters
75 meters
Questions & Step-by-Step Solutions
A person is standing 45 meters away from a building. If the angle of elevation to the top of the building is 45 degrees, what is the height of the building?
Correct Answer: 45 meters
Step 1: Understand the problem. You have a person standing 45 meters away from a building.
Step 2: Know that the angle of elevation to the top of the building is 45 degrees.
Step 3: Remember that 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: For an angle of 45 degrees, the tangent value is 1. This means height = distance.
Step 5: Calculate the height of the building using the formula: Height = distance * tan(angle).
Step 7: Since tan(45 degrees) = 1, the calculation becomes Height = 45 meters * 1.
Step 8: Therefore, the height of the building is 45 meters.
Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the building and the distance from it.
Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the building, the distance from the building, and the angle of elevation.
