A man is standing 50 meters away from a building. If the angle of elevation to t
Practice Questions
Q1
A man is standing 50 meters away from 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 man is standing 50 meters away from a building. If the angle of elevation to the top of the building is 60 degrees, what is the height of the building?
Correct Answer: 86.6 meters
Step 1: Understand the problem. A man is standing 50 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 man to the building (50 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 man to the building).
Step 4: Write the formula. The formula is: height = distance * tan(angle). Here, distance = 50 meters and angle = 60 degrees.
Step 5: Find the value of tan(60 degrees). The value of tan(60 degrees) is √3, which is approximately 1.732.
Step 6: Substitute the values into the formula. Height = 50 * tan(60 degrees) = 50 * √3.
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.
Angle of Elevation – Understanding how the angle of elevation from a point to the top of an object can be used to calculate height.
Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the building is the opposite side, the distance from the building is the adjacent side, and the angle of elevation is the angle between them.
