A person is standing at a distance of 40 meters from the base of a building. If
Practice Questions
Q1
A person is standing at a distance of 40 meters from the base of a building. If the angle of elevation to the top of the building is 60 degrees, what is the height of the building?
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Questions & Step-by-Step Solutions
A person is standing at a distance of 40 meters from the base of a building. If the angle of elevation to the top of the building is 60 degrees, what is the height of the building?
Step 1: Understand the problem. We have a person standing 40 meters away from a building and looking up at the top of the building at an angle of 60 degrees.
Step 2: Visualize the situation. Imagine a right triangle where one side is the height of the building, the other side is the distance from the person to the building (40 meters), and the angle between the ground and the line of sight to the top of the building is 60 degrees.
Step 3: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the building) divided by the adjacent side (distance from the person to the building). So, we write: tan(60°) = height / 40.
Step 4: Find the value of tan(60°). The value of tan(60°) is √3.
Step 5: Set up the equation. Now we have √3 = height / 40.
Step 6: Solve for height. Multiply both sides of the equation by 40 to isolate height: height = 40 * √3.
Step 7: Calculate the height. Using the approximate value of √3 (about 1.732), we find height ≈ 40 * 1.732 ≈ 69.28 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 the base.
Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the building, the distance from the base, and the angle of elevation.
