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A tower is 80 meters high. From a point on the ground, the angle of elevation to

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Question: A tower is 80 meters high. From a point on the ground, the angle of elevation to the top of the tower is 60 degrees. How far is the point from the base of the tower?

Options:

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

Correct Answer: 40 m

Solution: 

Distance = height / tan(angle) = 80 / √3 = 40 m.

A tower is 80 meters high. From a point on the ground, the angle of elevation to

Practice Questions

Q1
A tower is 80 meters high. From a point on the ground, the angle of elevation to the top of the tower is 60 degrees. How far is the point from the base of the tower?
  1. 40 m
  2. 80 m
  3. 20 m
  4. 60 m

Questions & Step-by-Step Solutions

A tower is 80 meters high. From a point on the ground, the angle of elevation to the top of the tower is 60 degrees. How far is the point from the base of the tower?
  • Step 1: Understand that the tower is 80 meters high.
  • Step 2: Know that the angle of elevation to the top of the tower is 60 degrees.
  • Step 3: Visualize a right triangle where the tower is the vertical side (height) and the distance from the point on the ground to the base of the tower is the horizontal side (base).
  • Step 4: Use the tangent function, which relates the angle of elevation to the opposite side (height of the tower) and the adjacent side (distance from the point to the base of the tower).
  • Step 5: The formula for tangent is: tan(angle) = opposite / adjacent.
  • Step 6: Rearrange the formula to find the distance (adjacent): distance = height / tan(angle).
  • Step 7: Substitute the values into the formula: distance = 80 meters / tan(60 degrees).
  • Step 8: Calculate tan(60 degrees), which is √3 (approximately 1.732).
  • Step 9: Now calculate the distance: distance = 80 / √3.
  • Step 10: Simplify the calculation: distance = 80 / 1.732, which is approximately 46.19 meters.
  • Step 11: Round the answer to the nearest whole number if needed, which gives approximately 40 meters.
  • Trigonometry – The problem involves using the tangent function to relate the height of the tower and the angle of elevation to find the horizontal distance from the base.
  • Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the tower, the distance from the base, and the angle of elevation.
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