Q43 of 68 Page 9

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 find the width of the lane.


Let AB and CD are the two buildings and AE and CE are the ladder


Hence, AE and CE = 26 m (given)


In the right Δ ABE, we have




⇒ BE = 13 m


Now, In ΔCED, we have







⇒ DE = 13√2 m


So, the width of the lane = BE + DE


= 13 + 13√2


= 13 (1 + √2)


= 13 (1 + 1.414) [∵√2 = 1.414]


= 13 × 2.414


= 31.38


= 31.4 m (approx.)


Hence, the width of the lane is 31.4 m (approx.)


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