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From a point on the ground, the angle of elevation to the top of a 20-meter tall

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Question: From a point on the ground, the angle of elevation to the top of a 20-meter tall pole is 60°. How far is the point from the base of the pole?

Options:

  1. 10 meters
  2. 20 meters
  3. 30 meters
  4. 40 meters

Correct Answer: 10 meters

Solution: 

Using tan(60°) = height/distance, distance = height/tan(60°) = 20/√3 = 10 meters.

From a point on the ground, the angle of elevation to the top of a 20-meter tall

Practice Questions

Q1
From a point on the ground, the angle of elevation to the top of a 20-meter tall pole is 60°. How far is the point from the base of the pole?
  1. 10 meters
  2. 20 meters
  3. 30 meters
  4. 40 meters

Questions & Step-by-Step Solutions

From a point on the ground, the angle of elevation to the top of a 20-meter tall pole is 60°. How far is the point from the base of the pole?
  • Step 1: Understand the problem. We have a pole that is 20 meters tall and we want to find out how far away from the pole we are standing.
  • Step 2: Identify the angle of elevation. The angle of elevation to the top of the pole is 60 degrees.
  • Step 3: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the pole) divided by the adjacent side (distance from the pole).
  • Step 4: Write the formula. We can write this as tan(60°) = height / distance.
  • Step 5: Plug in the values. We know the height is 20 meters, so we have tan(60°) = 20 / distance.
  • Step 6: Rearrange the formula to find distance. This gives us distance = height / tan(60°).
  • Step 7: Calculate tan(60°). The value of tan(60°) is √3.
  • Step 8: Substitute tan(60°) into the formula. Now we have distance = 20 / √3.
  • Step 9: Simplify the calculation. To make it easier, we can multiply the numerator and denominator by √3 to get distance = (20√3) / 3.
  • Step 10: Calculate the final distance. This gives us approximately 10 meters.
  • Trigonometric Ratios – Understanding the relationship between angles and sides in right triangles, specifically using the tangent function.
  • Angle of Elevation – The angle formed by the line of sight from the observer to the top of an object above the horizontal line.
  • Right Triangle Properties – Applying properties of right triangles to solve for unknown lengths using trigonometric functions.
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