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From a point on the ground, the angle of elevation to the top of a tower is 30 d

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Question: From a point on the ground, the angle of elevation to the top of a tower is 30 degrees. If the tower is 20 meters tall, how far is the point from the base of the tower?

Options:

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

Correct Answer: 20√3 meters

Solution: 

Using the tangent function, tan(30) = 20 / distance. Therefore, distance = 20 / tan(30) = 20√3 meters.

From a point on the ground, the angle of elevation to the top of a tower is 30 d

Practice Questions

Q1
From a point on the ground, the angle of elevation to the top of a tower is 30 degrees. If the tower is 20 meters tall, how far is the point from the base of the tower?
  1. 20√3 meters
  2. 10√3 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 tower is 30 degrees. If the tower is 20 meters tall, how far is the point from the base of the tower?
  • Step 1: Understand the problem. We have a tower that is 20 meters tall and we want to find out how far away a point on the ground is from the base of the tower.
  • Step 2: Identify the angle of elevation. The angle of elevation from the point on the ground to the top of the tower is 30 degrees.
  • Step 3: Use the tangent function. In a right triangle, the tangent of an angle is the opposite side (height of the tower) divided by the adjacent side (distance from the tower).
  • Step 4: Write the equation using the tangent function. We have tan(30 degrees) = height of the tower / distance from the tower.
  • Step 5: Substitute the known values into the equation. This gives us tan(30) = 20 / distance.
  • Step 6: Rearrange the equation to solve for distance. Multiply both sides by distance: distance * tan(30) = 20.
  • Step 7: Divide both sides by tan(30) to isolate distance. This gives us distance = 20 / tan(30).
  • Step 8: Calculate tan(30). The value of tan(30 degrees) is √3 / 3.
  • Step 9: Substitute tan(30) back into the equation. Now we have distance = 20 / (√3 / 3).
  • Step 10: Simplify the equation. This is the same as distance = 20 * (3 / √3) = 20√3 meters.
  • Trigonometric Ratios – Understanding how to use tangent, sine, and cosine functions to relate angles and sides in right triangles.
  • Angle of Elevation – Recognizing the angle formed by the horizontal line from the observer's eye to the line of sight to the top of an object.
  • Right Triangle Properties – Applying properties of right triangles to solve for unknown lengths using trigonometric functions.
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