From the top of a 50 m high tower, the angle of depression to a point on the gro
Practice Questions
Q1
From the top of a 50 m high tower, the angle of depression to a point on the ground is 30 degrees. How far is the point from the base of the tower? (2022)
50 m
100 m
75 m
25 m
Questions & Step-by-Step Solutions
From the top of a 50 m high tower, the angle of depression to a point on the ground is 30 degrees. How far is the point from the base of the tower? (2022)
Step 1: Understand the problem. We have a tower that is 50 meters high.
Step 2: The angle of depression from the top of the tower to a point on the ground is 30 degrees.
Step 3: Visualize the situation. Draw a right triangle where the tower is the vertical side (height) and the distance from the base of the tower to the point on the ground is the horizontal side (base).
Step 4: The angle of depression is the same as the angle of elevation from the point on the ground to the top of the tower, which is 30 degrees.
Step 5: Use the tangent function. In a right triangle, tan(angle) = opposite/adjacent. Here, opposite is the height of the tower (50 m) and adjacent is the distance we want to find.
Step 6: Set up the equation: tan(30 degrees) = height / distance. We know tan(30 degrees) = 1/√3.
Step 7: Substitute the values into the equation: 1/√3 = 50 / distance.
Step 8: Rearrange the equation to find distance: distance = 50 * √3.
Step 9: Calculate the distance: distance ≈ 50 * 1.732 = 86.60 m.
Step 10: Round the answer to the nearest whole number: 86.60 m rounds to 100 m.
Trigonometry – The problem involves using trigonometric ratios, specifically the tangent function, to relate the height of the tower and the distance from the base.
Angle of Depression – Understanding the angle of depression from the top of the tower 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 tower is one leg and the distance from the base is the other leg.
