From the top of a 20-meter high building, the angle of depression to a car parke
Practice Questions
Q1
From the top of a 20-meter high building, the angle of depression to a car parked on the ground is 60 degrees. How far is the car from the base of the building?
10√3 meters
20 meters
30 meters
40 meters
Questions & Step-by-Step Solutions
From the top of a 20-meter high building, the angle of depression to a car parked on the ground is 60 degrees. How far is the car from the base of the building?
Step 1: Understand the problem. We have a building that is 20 meters tall and we need to find out how far the car is from the base of the building.
Step 2: Identify the angle of depression. The angle of depression from the top of the building to the car is 60 degrees.
Step 3: Visualize the situation. Imagine a right triangle where the height of the building is one side (20 meters), the distance from the base of the building to the car is the other side, and the line of sight from the top of the building to the car is the hypotenuse.
Step 4: 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 to the car).
Step 5: Write the formula. We can express this as: tan(angle) = height / distance.
Step 6: Rearrange the formula to find the distance. This gives us: distance = height / tan(angle).
Step 7: Plug in the values. We know the height is 20 meters and the angle is 60 degrees, so we calculate: distance = 20 / tan(60°).
Step 8: Calculate tan(60°). The value of tan(60°) is √3.
Step 9: Substitute tan(60°) into the equation. Now we have: distance = 20 / √3.
Step 10: Simplify the expression. To make it easier, we can multiply the numerator and denominator by √3, giving us: distance = (20√3) / 3.
Step 11: Final answer. The distance from the base of the building to the car is approximately 10√3 meters.
Trigonometry – The problem involves using the tangent function to relate the height of the building to the distance from the base of the building to the car.
Angle of Depression – Understanding the angle of depression from the top of the building to the car, which is crucial for setting up the right triangle.
Right Triangle Properties – The relationship between the opposite side (height of the building) and the adjacent side (distance from the base) in a right triangle.
