The angle of elevation of a 5 m long ladder leaning against a wall is 45 degrees and the foot of the ladder is 3 m away from the…

Question

The angle of elevation of a 5 m long ladder leaning against a wall is 45 degrees and the foot of the ladder is 3 m away from the wall. The height of the wall up to the point where the ladder is resting against it is:

1. A. 2 m
2. B. 3 m
3. C. 4 m (Correct answer)
4. D. Cannot be determined on the basis of the given information

Correct Answer

Option C — 4 m

Detailed Solution & Explanation

The correct answer is 4 m.

Key Points

• The ladder is 5 m long, foot is 3 m from the wall, angle of elevation = 45°.
• Using Pythagoras: height² = 5² − 3² = 25 − 9 = 16 → height = 4 m. Note: the problem states angle = 45° but the geometry (3-4-5 right triangle) gives angle = arctan(4/3) ≈ 53°.
• The answer from Pythagorean theorem is 4 m.