A person standing 50 meters away from a building observes the top of the buildin
Practice Questions
Q1
A person standing 50 meters 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?
25√3 meters
50 meters
75 meters
100 meters
Questions & Step-by-Step Solutions
A person standing 50 meters 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?
Correct Answer: 25√3 meters
Step 1: Understand the situation. A person is standing 50 meters away from a building and looking up at the top of the building.
Step 2: Identify the angle of elevation. The angle at which the person looks up to see 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 building).
Step 4: Write the formula. The formula to find the height (h) of the building is: h = distance * tan(angle).
Step 5: Plug in the values. The distance is 50 meters and the angle is 60 degrees. So, h = 50 * tan(60 degrees).
Step 6: Calculate tan(60 degrees). The value of tan(60 degrees) is √3.
Step 7: Complete the calculation. So, h = 50 * √3.
Step 8: Simplify the result. The height of the building is 50√3 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 it.
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 given.
