From the top of a 50 m high building, the angle of depression to a point on the
Practice Questions
Q1
From the top of a 50 m high building, the angle of depression to a point on the ground is 45 degrees. How far is the point from the base of the building?
25 m
50 m
70 m
100 m
Questions & Step-by-Step Solutions
From the top of a 50 m high building, the angle of depression to a point on the ground is 45 degrees. How far is the point from the base of the building?
Correct Answer: 50 m
Step 1: Understand that the angle of depression is the angle formed between the horizontal line from the top of the building and the line of sight to the point on the ground.
Step 2: Recognize that the height of the building is 50 meters.
Step 3: Note that the angle of depression is 45 degrees.
Step 4: In a right triangle formed by the height of the building and the distance from the base of the building to the point on the ground, the opposite side is the height (50 m) and the adjacent side is the distance we want to find.
Step 5: Use the tangent function, which relates the opposite side to the adjacent side: tan(angle) = opposite/adjacent.
Step 6: Substitute the known values into the equation: tan(45°) = height/distance.
Step 7: Since tan(45°) equals 1, we have 1 = 50/distance.
Step 8: Rearrange the equation to find the distance: distance = 50 m.
Angle of Depression – The angle formed by a horizontal line and the line of sight to a point below the horizontal line.
Trigonometric Ratios – Using tangent to relate the height of the building and the distance from the base.
Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the building and the distance to the point on the ground.
