A man is standing 40 meters away from a building. If the angle of elevation to t
Practice Questions
Q1
A man is standing 40 meters away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?
20√3 meters
40√3 meters
30 meters
20 meters
Questions & Step-by-Step Solutions
A man is standing 40 meters away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?
Step 1: Understand the problem. A man is standing 40 meters away from a building and looking up at the top of the building at an angle of 30 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 (40 meters), and the angle between the ground and the line of sight to the top of the building is 30 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 = 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. This simplifies to height = 40/√3.
Step 8: To make it easier to understand, multiply the numerator and denominator by √3. This gives height = (40√3)/3.
Step 9: The final answer is approximately 20√3 meters, which is the height of the building.
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 – Understanding the relationship between the sides of a right triangle formed by the height of the building, the distance from the building, and the angle of elevation.
