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Q.

A ladder of length $6 m$ makes an angle of $45 °$ 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 $60 °$ with the floor. Find the distance between these two walls of the room.

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a

3 (1 + 3) m

b

3 (1 + 2) m

c

3 (1 + 5) m

d

4 (1 + 2) m

answer is B.

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Detailed Solution

Given that a ladder of length 6m makes an angle of

45 °

with the floor while leaning against one wall of a room.
We have to find the distance between the two walls of the room.
A ladder of length 6 metres makes an angle of 45^(@) with the floor while leaning against one wall of a room. If the foot of the ladder is kept fixed on

A ladder of length 6 metres makes an angle of 45^(@) with the floor while leaning against one wall of a room. If the foot of the ladder is kept fixed on

The value for

tan 30 ° = 13 .

Suppose, the foot of the ladder be fixed at the point O. Then, by using the figure geometry,
Question Image

Question Image

From the equation (1) and (2), the distance between the two walls of the room is,

B D = B O + D O ⇒ B D = 3 + 32 ⇒ B D = 3 (1 + 2) m

The required solution is

3 (1 + 2) m

.
Therefore, the correct option is 2.

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A ladder of length 6 m makes an angle of 45 ° 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 60 ° with the floor. Find the distance between these two walls of the room.