A person standing 40 meters away from a building observes the angle of elevation
Practice Questions
Q1
A person standing 40 meters away from a building observes the angle of elevation to the top of the building as 30 degrees. What is the height of the building? (2022)
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10 m
15 m
25 m
Questions & Step-by-Step Solutions
A person standing 40 meters away from a building observes the angle of elevation to the top of the building as 30 degrees. What is the height of the building? (2022)
Step 1: Understand the problem. You are standing 40 meters away from a building and looking up at the top of the building, forming an angle of 30 degrees with the ground.
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 the base (40 meters), and the height of the building is the vertical side.
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. Here, the angle is 30 degrees, the opposite side is the height (H), and the adjacent side is 40 meters. So, tan(30) = H / 40.
Step 5: Calculate tan(30). The value of tan(30 degrees) is 1/√3 (approximately 0.577).
Step 6: Rewrite the equation: H = 40 * tan(30). Substitute tan(30) with 1/√3: H = 40 * (1/√3).
Step 7: Calculate the height: H = 40 * (1/√3) ≈ 40 * 0.577 ≈ 23.09 meters.
Step 8: Round the height to the nearest whole number, which is approximately 23 meters.
Trigonometry – The problem tests the understanding of basic trigonometric functions, specifically the tangent function, in relation to right triangles.
Angle of Elevation – The question involves interpreting the angle of elevation from a horizontal line to the top of a building.
Distance and Height Relationship – It assesses the ability to relate horizontal distance and vertical height using trigonometric ratios.
