A person is standing 50 meters away from a statue. If the angle of elevation to
Practice Questions
Q1
A person is standing 50 meters away from a statue. If the angle of elevation to the top of the statue is 45 degrees, what is the height of the statue?
25 meters
50 meters
35 meters
45 meters
Questions & Step-by-Step Solutions
A person is standing 50 meters away from a statue. If the angle of elevation to the top of the statue is 45 degrees, what is the height of the statue?
Correct Answer: 50 meters
Step 1: Understand the situation. A person is standing 50 meters away from a statue.
Step 2: Know that the angle of elevation to the top of the statue is 45 degrees.
Step 3: Remember that the angle of elevation is the angle formed between the horizontal line (the ground) and the line of sight to the top of the statue.
Step 4: Use the tangent function in trigonometry, which relates the angle to the opposite side (height of the statue) and the adjacent side (distance from the statue).
Step 5: The formula for height is: Height = distance * tan(angle).
Step 6: Plug in the values: Height = 50 meters * tan(45 degrees).
Step 9: Conclude that the height of the statue is 50 meters.
Trigonometry – The problem involves using the tangent function to relate the height of the statue to the distance from the observer and the angle of elevation.
Angle of Elevation – Understanding that the angle of elevation is measured from the horizontal line of sight to the top of the object.
Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the statue is the opposite side, the distance is the adjacent side, and the angle is given.
