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From a point on the ground, the angle of elevation to the top of a hill is 45 de

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Question: From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 40 m, how far is the point from the base of the hill?

Options:

  1. 20 m
  2. 40 m
  3. 60 m
  4. 80 m

Correct Answer: 40 m

Solution: 

Using tan(45°) = height/distance, we have 1 = 40/distance. Therefore, distance = 40 m.

From a point on the ground, the angle of elevation to the top of a hill is 45 de

Practice Questions

Q1
From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 40 m, how far is the point from the base of the hill?
  1. 20 m
  2. 40 m
  3. 60 m
  4. 80 m

Questions & Step-by-Step Solutions

From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 40 m, how far is the point from the base of the hill?
  • Step 1: Understand that the angle of elevation is the angle formed between the horizontal ground and the line of sight to the top of the hill.
  • Step 2: Note that the angle of elevation is given as 45 degrees.
  • Step 3: Recall the definition of the tangent function in a right triangle: tan(angle) = opposite side / adjacent side.
  • Step 4: In this scenario, the 'opposite side' is the height of the hill (40 m) and the 'adjacent side' is the distance from the point on the ground to the base of the hill.
  • Step 5: Set up the equation using the tangent function: tan(45°) = height / distance.
  • Step 6: Substitute the known values into the equation: tan(45°) = 40 / distance.
  • Step 7: Since tan(45°) equals 1, rewrite the equation as 1 = 40 / distance.
  • Step 8: To find the distance, rearrange the equation: distance = 40 / 1.
  • Step 9: Calculate the distance: distance = 40 m.
  • Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height and distance from the base of the hill.
  • Right Triangle Properties – Understanding the properties of right triangles, specifically how to apply the tangent ratio in a right triangle scenario.
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