Question

A ladder of length 4m makes an angle 30⁰ with the floor while leaning against one wall of a room. If the foot of the ladder is kept fixed on the floor and it is made to lean against the opposite wall of the room, it makes an angle of 60⁰ with the floor. Find the distance between the two walls of the room.

Answer 1

To find the distance between the two walls of the room, we can use the trigonometric ratios of sine and cosine.

1. Length of the ladder: 4 meters

2. Angle the ladder makes with the floor (first position): 30 degrees

3. Angle the ladder makes with the floor (second position): 60 degrees

To find the distance between the two walls of the room, we can use the formula:

Distance = Length of the ladder * sin(Angle)

Using this formula:

Distance (first position) = 4 meters * sin(30 degrees)

Distance (second position) = 4 meters * sin(60 degrees)

Calculating the distances:

Distance (first position) = 4 meters * 0.5 = 2 meters

Distance (second position) = 4 meters * √3/2 ≈ 3.464 meters

Therefore, the distance between the two walls of the room is approximately 2 meters in the first position and approximately 3.464 meters in the second position.

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