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A ladder 25 meters long leans against a wall. If the foot of the ladder is 7 met

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Question: A ladder 25 meters long leans against a wall. If the foot of the ladder is 7 meters from the wall, what is the angle of elevation of the ladder?

Options:

  1. 30 degrees
  2. 45 degrees
  3. 60 degrees
  4. 75 degrees

Correct Answer: 60 degrees

Solution: 

Using cos(θ) = adjacent/hypotenuse, cos(θ) = 7/25. Therefore, θ = cos⁻¹(7/25) which is approximately 60 degrees.

A ladder 25 meters long leans against a wall. If the foot of the ladder is 7 met

Practice Questions

Q1
A ladder 25 meters long leans against a wall. If the foot of the ladder is 7 meters from the wall, what is the angle of elevation of the ladder?
  1. 30 degrees
  2. 45 degrees
  3. 60 degrees
  4. 75 degrees

Questions & Step-by-Step Solutions

A ladder 25 meters long leans against a wall. If the foot of the ladder is 7 meters from the wall, what is the angle of elevation of the ladder?
  • Step 1: Understand the problem. We have a ladder that is 25 meters long leaning against a wall, and the foot of the ladder is 7 meters away from the wall.
  • Step 2: Identify the triangle formed by the ladder, the wall, and the ground. The ladder is the hypotenuse, the distance from the wall is the adjacent side, and the height of the ladder on the wall is the opposite side.
  • Step 3: Use the cosine function to find the angle of elevation (θ). The formula is cos(θ) = adjacent/hypotenuse.
  • Step 4: Substitute the known values into the formula. Here, the adjacent side is 7 meters and the hypotenuse is 25 meters. So, cos(θ) = 7/25.
  • Step 5: To find the angle θ, use the inverse cosine function. This means θ = cos⁻¹(7/25).
  • Step 6: Calculate the value of θ using a calculator. This will give you the angle of elevation of the ladder.
  • Trigonometry – The question tests the understanding of trigonometric ratios, specifically the cosine function, in a right triangle formed by the ladder, the wall, and the ground.
  • Right Triangle Properties – It assesses the ability to identify the sides of a right triangle (adjacent, opposite, hypotenuse) and apply the Pythagorean theorem if necessary.
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