AB is a ladder of length 4m, leaning on a vertical wall. End A of the ladder is on the floor and end B is on the wall. If the ladder slipped to the position A′B′, the top end of the ladder has come down by ___.(Take √3=1.73)
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Solution
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Given, AB=A′B′=4m ∠BAW=60∘ ∠B′A′W=30∘ Now, in △ABW
sin60∘=BWAB
⇒√32=BW4 ⇒BW=2√3 Now, in △A′B′W sin30∘=B′WA′B′
⇒12=B′W4 ⇒B′W=2 We know,
B′B=BW−B′W=2√3−2
=2(√3−1)m
=2(1.73−1)m
=1.46m
So, the required answer is 1.46m.
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