From the top of a 50-meter high building, the angle of depression to a point on
Practice Questions
Q1
From the top of a 50-meter high building, the angle of depression to a point on the ground is 30 degrees. How far is the point from the base of the building?
25√3 meters
50 meters
75 meters
100 meters
Questions & Step-by-Step Solutions
From the top of a 50-meter high building, the angle of depression to a point on the ground is 30 degrees. How far is the point from the base of the building?
Correct Answer: 50√3 meters
Step 1: Understand the problem. We have a building that is 50 meters tall.
Step 2: The angle of depression from the top of the building to a point on the ground is 30 degrees.
Step 3: Visualize the situation. Draw a right triangle where the height of the building is one side (50 meters), the distance from the base of the building to the point on the ground is the other side, and the line of sight from the top of the building to the point on the ground is the hypotenuse.
Step 4: Use the tangent function. In a right triangle, the tangent of an angle is the opposite side (height of the building) divided by the adjacent side (distance from the base).
Step 6: We know the height is 50 meters and tan(30 degrees) is 1/√3.
Step 7: Set up the equation: 1/√3 = 50 / distance.
Step 8: Rearrange the equation to find distance: distance = height / tan(30 degrees).
Step 9: Substitute the values: distance = 50 / (1/√3).
Step 10: Simplify the equation: distance = 50 * √3.
Step 11: Calculate the final answer: distance = 50√3 meters.
Trigonometry – The problem involves using the tangent function to relate the height of the building to the angle of depression and the horizontal distance from the base.
Angle of Depression – Understanding that the angle of depression from the top of the building to the point on the ground is equal to the angle of elevation from that point to the top of the building.
Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the building is one leg, the distance from the base is the other leg, and the line of sight forms the hypotenuse.
