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From the top of a hill, the angle of depression to a car parked on the ground is

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Question: From the top of a hill, the angle of depression to a car parked on the ground is 45 degrees. If the height of the hill is 100 meters, how far is the car from the base of the hill?

Options:

  1. 100 meters
  2. 150 meters
  3. 200 meters
  4. 250 meters

Correct Answer: 100 meters

Solution: 

Distance = height / tan(angle) = 100 / 1 = 100 meters.

From the top of a hill, the angle of depression to a car parked on the ground is

Practice Questions

Q1
From the top of a hill, the angle of depression to a car parked on the ground is 45 degrees. If the height of the hill is 100 meters, how far is the car from the base of the hill?
  1. 100 meters
  2. 150 meters
  3. 200 meters
  4. 250 meters

Questions & Step-by-Step Solutions

From the top of a hill, the angle of depression to a car parked on the ground is 45 degrees. If the height of the hill is 100 meters, how far is the car from the base of the hill?
Correct Answer: 100 meters
  • Step 1: Understand the problem. We have a hill that is 100 meters tall.
  • Step 2: The angle of depression from the top of the hill to the car is 45 degrees.
  • Step 3: Visualize the situation. Draw a right triangle where the height of the hill is one side (100 meters) and the distance from the base of the hill to the car is the other side.
  • Step 4: Recall the definition of the angle of depression. It is the angle formed between the horizontal line from the top of the hill and the line of sight to the car.
  • Step 5: Since the angle of depression is 45 degrees, the angle at the base of the triangle (where the car is) is also 45 degrees because of alternate interior angles.
  • Step 6: Use the tangent function. The tangent of an angle in a right triangle is the opposite side (height of the hill) divided by the adjacent side (distance from the base of the hill to the car).
  • Step 7: Write the formula: tan(angle) = opposite / adjacent. Here, tan(45 degrees) = height / distance.
  • Step 8: We know that tan(45 degrees) = 1. So, we can set up the equation: 1 = 100 / distance.
  • Step 9: Rearrange the equation to find the distance: distance = 100 / 1.
  • Step 10: Calculate the distance: distance = 100 meters.
  • Angle of Depression – The angle formed by a horizontal line and the line of sight to an object below the horizontal line.
  • Trigonometric Ratios – Using tangent to relate the height of the hill and the distance to the car.
  • Right Triangle Properties – Understanding the relationship between the height of the hill, the distance from the base, and the angle of depression.
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