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A tower is 120 meters high. From a point on the ground, the angle of elevation t

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Question: A tower is 120 meters high. From a point on the ground, the angle of elevation to the top of the tower is 45 degrees. How far is the point from the base of the tower? (2020)

Options:

  1. 60 m
  2. 120 m
  3. 90 m
  4. 30 m

Correct Answer: 120 m

Exam Year: 2020

Solution: 

Distance = Height / tan(45) = 120 / 1 = 120 m.

A tower is 120 meters high. From a point on the ground, the angle of elevation t

Practice Questions

Q1
A tower is 120 meters high. From a point on the ground, the angle of elevation to the top of the tower is 45 degrees. How far is the point from the base of the tower? (2020)
  1. 60 m
  2. 120 m
  3. 90 m
  4. 30 m

Questions & Step-by-Step Solutions

A tower is 120 meters high. From a point on the ground, the angle of elevation to the top of the tower is 45 degrees. How far is the point from the base of the tower? (2020)
  • Step 1: Understand that the tower is 120 meters high.
  • Step 2: Know that the angle of elevation to the top of the tower is 45 degrees.
  • Step 3: Recall that the tangent of an angle in a right triangle is the opposite side (height of the tower) divided by the adjacent side (distance from the base).
  • Step 4: Write the formula: Distance = Height / tan(angle).
  • Step 5: Substitute the values into the formula: Distance = 120 meters / tan(45 degrees).
  • Step 6: Know that tan(45 degrees) equals 1.
  • Step 7: Calculate the distance: Distance = 120 meters / 1.
  • Step 8: Conclude that the distance from the point to the base of the tower is 120 meters.
  • Trigonometry – The problem involves using the tangent function to relate the height of the tower and the distance from the point on the ground.
  • Angle of Elevation – Understanding the angle of elevation is crucial for setting up the right triangle in this scenario.
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