From a point on the ground, the angle of elevation to the top of a 50-meter tall
Practice Questions
Q1
From a point on the ground, the angle of elevation to the top of a 50-meter tall building is 45 degrees. How far is the point from the base of the building?
50 meters
25 meters
35 meters
40 meters
Questions & Step-by-Step Solutions
From a point on the ground, the angle of elevation to the top of a 50-meter tall building is 45 degrees. How far is the point from the base of the building?
Correct Answer: 50 meters
Step 1: Understand that the angle of elevation is the angle formed between the horizontal line from the observer's eye to the top of the building.
Step 2: Recognize that the height of the building is 50 meters.
Step 3: Note that the angle of elevation is 45 degrees.
Step 4: Use the tangent function, which relates the angle of elevation to the opposite side (height of the building) and the adjacent side (distance from the building).
Step 5: Recall that tan(45 degrees) equals 1.
Step 6: Set up the equation: distance = height / tan(angle).
Step 7: Substitute the values into the equation: distance = 50 meters / tan(45 degrees).
Step 8: Since tan(45 degrees) is 1, the equation simplifies to: distance = 50 meters / 1.
Step 9: Calculate the distance, which equals 50 meters.
Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height and distance from the building.
Angle of Elevation – Understanding how the angle of elevation relates to the height of the building and the horizontal distance from the observer.
