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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 point is 10 meters away from the base of the tower, what is the height of the tower?

Options:

  1. 5 m
  2. 8.66 m
  3. 10 m
  4. 17.32 m

Correct Answer: 17.32 m

Solution: 

Height = 10 * tan(30) = 10 * (1/√3) = 10 * 0.577 = 5.77 m

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 point is 10 meters away from the base of the tower, what is the height of the tower?
  1. 5 m
  2. 8.66 m
  3. 10 m
  4. 17.32 m

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 point is 10 meters away from the base of the tower, what is the height of the tower?
  • Step 1: Understand the problem. We have a tower and a point on the ground that is 10 meters away from the base of the tower.
  • Step 2: Identify the angle of elevation. The angle from the point on the ground to the top of the tower is 30 degrees.
  • Step 3: Recall the relationship in a right triangle. The height of the tower is opposite the angle, and the distance from the point to the base of the tower is adjacent to the angle.
  • Step 4: Use the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side (height of the tower) to the adjacent side (distance from the point to the base).
  • Step 5: Write the formula. We can express this as: tan(30 degrees) = height / 10 meters.
  • Step 6: Solve for height. Rearranging the formula gives us: height = 10 meters * tan(30 degrees).
  • Step 7: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3 or approximately 0.577.
  • Step 8: Multiply to find the height. So, height = 10 * 0.577 = 5.77 meters.
  • Trigonometry – The problem tests the understanding of basic trigonometric functions, specifically the tangent function, which relates the angle of elevation to the opposite and adjacent sides of a right triangle.
  • Right Triangle Properties – The question involves identifying the right triangle formed by the height of the tower, the distance from the point to the base, and the line of sight to the top of the tower.
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