A person standing 40 meters away from a building observes the top of the buildin
Practice Questions
Q1
A person standing 40 meters away from a building observes the top of the building at an angle of elevation of 30 degrees. What is the height of the building?
20 meters
10√3 meters
30 meters
40 meters
Questions & Step-by-Step Solutions
A person standing 40 meters away from a building observes the top of the building at an angle of elevation of 30 degrees. What is the height of the building?
Correct Answer: 10√3 meters
Step 1: Understand the situation. A person is standing 40 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 30 degrees.
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. Height = distance * tan(angle). Here, distance = 40 meters and angle = 30 degrees.
Step 5: Find the value of tan(30 degrees). The value of tan(30 degrees) is 1/√3.
Step 6: Substitute the values into the formula. Height = 40 * (1/√3).
Step 7: Calculate the height. Height = 40/√3.
Step 8: Simplify the height. Height = 10√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 the observer.
Angle of Elevation – Understanding how to interpret the angle of elevation from a horizontal line to the top of an object.
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.
