From the top of a 60 m high building, the angle of depression to a point on the
Practice Questions
Q1
From the top of a 60 m 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?
60√3 m
30√3 m
60 m
30 m
Questions & Step-by-Step Solutions
From the top of a 60 m 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?
Step 1: Understand the problem. We have a building that is 60 meters high.
Step 2: Identify the angle of depression, which is 30 degrees.
Step 3: Visualize the situation. The angle of depression means we are looking down from the top of the building to a point on the ground.
Step 4: Recognize that we can form a right triangle. The height of the building is one side (60 m), and the distance from the base of the building to the point on the ground is the other side.
Step 5: Use the tangent function. In a right triangle, the tangent of an angle is the opposite side (height) divided by the adjacent side (distance).
Step 6: Write the equation: tan(30°) = height / distance.
Step 7: Substitute the known values into the equation: tan(30°) = 60 / distance.
Step 8: Rearrange the equation to find distance: distance = height / tan(30°).
Step 9: Calculate tan(30°). It is equal to 1/√3.
Step 10: Substitute tan(30°) into the equation: distance = 60 / (1/√3).
Step 11: Simplify the equation: distance = 60 * √3.
Step 12: The final answer is distance = 60√3 meters.
Trigonometry – The problem involves using trigonometric ratios, specifically the tangent function, to relate the height of the building to the distance from its base.
Angle of Depression – Understanding the angle of depression from the top of the building to the point on the ground is crucial for setting up the problem correctly.
Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the building is one leg and the distance from the base is the other leg.
