A person is standing 40 meters away from a building. If the angle of elevation t
Practice Questions
Q1
A person is standing 40 meters away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?
20 meters
23 meters
30 meters
35 meters
Questions & Step-by-Step Solutions
A person is standing 40 meters away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?
Correct Answer: 23.09 meters
Step 1: Understand the problem. You have a person standing 40 meters away from a building and looking up at the top of the building at an angle of 30 degrees.
Step 2: Identify the right triangle formed by the person, the top of the building, and the base of the building. The distance from the person to the building is the base of the triangle.
Step 3: The angle of elevation (30 degrees) is the angle between the line of sight to the top of the building and the horizontal line from the person to the building.
Step 4: Use the tangent function, which relates the angle of a right triangle to the opposite side (height of the building) and the adjacent side (distance from the building). The formula is: tan(angle) = opposite/adjacent.
Step 5: Rearrange the formula to find the height (opposite side): height = distance * tan(angle).
Step 6: Plug in the values: height = 40 meters * tan(30 degrees).
Step 7: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3 or approximately 0.577.
Step 8: Now calculate the height: height = 40 * (1/√3).
Step 9: Simplify the calculation: height = 40 / 1.732 (since √3 is approximately 1.732).
Step 10: Perform the division: height ≈ 23.09 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.
