A man is standing 100 meters away from a building. If the angle of elevation to
Practice Questions
Q1
A man is standing 100 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?
100 m
50 m
75 m
25 m
Questions & Step-by-Step Solutions
A man is standing 100 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?
Step 1: Understand the problem. A man is standing 100 meters away from a building.
Step 2: Identify the angle of elevation to the top of the building, which is 45 degrees.
Step 3: Recall the tangent function in trigonometry: tan(angle) = opposite side / adjacent side.
Step 4: In this scenario, the 'opposite side' is the height of the building, and the 'adjacent side' is the distance from the man to the building (100 meters).
Step 5: Write the equation using the tangent function: tan(45°) = height / 100.
Step 6: Know that tan(45°) equals 1. So, the equation becomes: 1 = height / 100.
Step 7: To find the height, multiply both sides of the equation by 100: height = 100 * 1.
Step 8: Calculate the height: height = 100 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.
Angle of Elevation – Understanding how the angle of elevation relates to the height and distance in a right triangle.
