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Q.

A ladder is placed against a building, and the angle of elevation of the top of the ladder is 60°  The ladder is turned so that it is placed against another building on the other side of the lane and the angle of elevation, in this case, is 45°  . If the ladder is 26 m long, then what will be the width of the lane?


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a

30.1m

b

31.4m

c

29.8m

d

30m 

answer is B.

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Detailed Solution

Given that,
The length of the ladder AC=26   m and CD=26   m
We draw a schematic diagram,
Question ImageApplying the cosine rule cosθ= base hypotenuse   in ΔABC  ,
cos 60 ° = BC AC ⇒ 1 2 = BC 26     [∵cos 60 ° = 1 2 ] ⇒BC= 26 2 ⇒BC=13 m  
Applying the cosine rule in ΔCDE  ,
Question ImageThe width of the lane BE,
Adding the values BC=13   m and CE=13 2  m to get the width of the lane BE,
BE=BC+CE ⇒BE=13+13 2 ⇒BE=13 1+ 2   ⇒BE=13 1+1.414 ⇒BE=13 2.414 ⇒BE=31.4 m  
Thus the width of the lane will be 31.4   m.
Therefore the correct option is 2.
 
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