If a person standing 30 m away from a building observes the top of the building
Practice Questions
Q1
If a person standing 30 m away from a building observes the top of the building at an angle of elevation of 60 degrees, what is the height of the building? (2023)
15 m
25 m
30 m
51.96 m
Questions & Step-by-Step Solutions
If a person standing 30 m away from a building observes the top of the building at an angle of elevation of 60 degrees, what is the height of the building? (2023)
Step 1: Understand the problem. We have a person standing 30 meters away from a building and looking up at the top of the building at an angle of 60 degrees.
Step 2: Identify the right triangle formed. The distance from the person to the building is one side (30 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. The tangent of an angle in a right triangle is the opposite side (height of the building) divided by the adjacent side (distance from the building).
Step 4: Write the formula. For our case, tan(60 degrees) = height / 30 m.
Step 5: Rearrange the formula to find the height. Height = 30 m * tan(60 degrees).
Step 6: Calculate tan(60 degrees). The value of tan(60 degrees) is √3, which is approximately 1.732.
Step 7: Substitute the value into the formula. Height = 30 m * 1.732.
Step 8: Perform the multiplication. Height ≈ 30 * 1.732 = 51.96 m.
Trigonometry – The problem tests the understanding of the tangent function in right triangles, specifically how to calculate height using the angle of elevation.
Angle of Elevation – The question involves interpreting the angle of elevation from a horizontal line to the top of the building.
Right Triangle Properties – The scenario describes a right triangle formed by the height of the building, the distance from the observer to the building, and the line of sight.
