A person is standing 40 m away from a building. If the angle of elevation to the
Practice Questions
Q1
A person is standing 40 m 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 m
40 m
30 m
10 m
Questions & Step-by-Step Solutions
A person is standing 40 m 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?
Step 1: Understand the problem. You are 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 your position, the top of the building, and the base of the building. The distance from you to the building is one side (40 m), the height of the building is the other side, and the line of sight to the top of the building is the hypotenuse.
Step 3: 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). The formula is: tan(angle) = opposite/adjacent.
Step 4: Plug in the values into the formula. For an angle of 30 degrees, the formula becomes: tan(30°) = height / 40 m.
Step 5: Rearrange the formula to find the height: height = 40 m * tan(30°).
Step 6: Calculate tan(30°). The value of tan(30°) is 1/√3 (approximately 0.577).
Step 7: Multiply the distance by the tangent value: height = 40 m * (1/√3).
Step 8: Calculate the height: height ≈ 40 m * 0.577 ≈ 23.1 m.
Step 9: Round the height to a reasonable number. The height of the building is approximately 20 m.
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.
