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A man is standing on a hill 100 meters high. If he looks down at an angle of 45

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Question: A man is standing on a hill 100 meters high. If he looks down at an angle of 45 degrees, how far is he from the base of the hill? (2020)

Options:

  1. 100 meters
  2. 50 meters
  3. 70 meters
  4. 30 meters

Correct Answer: 100 meters

Exam Year: 2020

Solution: 

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

A man is standing on a hill 100 meters high. If he looks down at an angle of 45

Practice Questions

Q1
A man is standing on a hill 100 meters high. If he looks down at an angle of 45 degrees, how far is he from the base of the hill? (2020)
  1. 100 meters
  2. 50 meters
  3. 70 meters
  4. 30 meters

Questions & Step-by-Step Solutions

A man is standing on a hill 100 meters high. If he looks down at an angle of 45 degrees, how far is he from the base of the hill? (2020)
  • Step 1: Understand that the man is looking down from a height of 100 meters.
  • Step 2: Recognize that he is looking down at an angle of 45 degrees.
  • Step 3: Recall that the tangent of an angle in a right triangle is the opposite side (height) divided by the adjacent side (distance from the base).
  • Step 4: For a 45-degree angle, the tangent value is 1 (tan(45 degrees) = 1).
  • Step 5: Use the formula: Distance = height / tan(angle).
  • Step 6: Plug in the values: Distance = 100 meters / 1.
  • Step 7: Calculate the distance: Distance = 100 meters.
  • Trigonometry – The question tests the understanding of basic trigonometric functions, specifically the tangent function, which relates the angle of elevation or depression to the opposite and adjacent sides of a right triangle.
  • Right Triangle Properties – The problem involves a right triangle formed by the height of the hill, the distance from the man to the base of the hill, and the line of sight.
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