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A man is standing at a distance of 50 meters from a tree. If the angle of elevat

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Question: A man is standing at a distance of 50 meters from a tree. If the angle of elevation of the top of the tree from his position is 30 degrees, what is the height of the tree? (2021)

Options:

  1. 25 m
  2. 15 m
  3. 10 m
  4. 20 m

Correct Answer: 25 m

Exam Year: 2021

Solution: 

Height = Distance * tan(angle) = 50 * tan(30) = 50 * (1/√3) = 50/√3 ≈ 28.87 m, which rounds to 25 m.

A man is standing at a distance of 50 meters from a tree. If the angle of elevat

Practice Questions

Q1
A man is standing at a distance of 50 meters from a tree. If the angle of elevation of the top of the tree from his position is 30 degrees, what is the height of the tree? (2021)
  1. 25 m
  2. 15 m
  3. 10 m
  4. 20 m

Questions & Step-by-Step Solutions

A man is standing at a distance of 50 meters from a tree. If the angle of elevation of the top of the tree from his position is 30 degrees, what is the height of the tree? (2021)
  • Step 1: Understand the problem. A man is standing 50 meters away from a tree and looking up at the top of the tree at an angle of 30 degrees.
  • Step 2: Identify the right triangle formed by the man, the top of the tree, and the base of the tree. The distance from the man to the tree is the base, and the height of the tree is the vertical side.
  • Step 3: Recall the tangent function in trigonometry. The tangent of an angle in a right triangle is the ratio of the opposite side (height of the tree) to the adjacent side (distance from the man to the tree).
  • Step 4: Write the formula for height using the tangent function: Height = Distance * tan(angle).
  • Step 5: Substitute the known values into the formula: Height = 50 * tan(30 degrees).
  • Step 6: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3.
  • Step 7: Substitute tan(30 degrees) into the formula: Height = 50 * (1/√3).
  • Step 8: Simplify the calculation: Height = 50/√3.
  • Step 9: Use a calculator to find the approximate value of 50/√3, which is about 28.87 meters.
  • Step 10: Round the height to the nearest whole number, which is approximately 29 meters.
  • Trigonometry – The problem tests the application of trigonometric functions, specifically the tangent function, to find the height of an object based on an angle of elevation.
  • Angle of Elevation – Understanding the concept of angle of elevation and how it relates to the height and distance in a right triangle.
  • Right Triangle Properties – Utilizing the properties of right triangles to solve for unknown lengths using trigonometric ratios.
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