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Question

A carpenter makes stools for electricians with a square top of side 0.5m and at a height 1.5m above the ground. Also, each leg is inclined at an angle of 60 to the ground. The lengths of two steps in metres correct up to two places of decimals is 


  1. 1.045, 1.782 m

  2. 1.122, 1.901 m

  3. 1.077, 1.653 m

  4. 1.324, 1.890 m


Solution

The correct option is C

1.077, 1.653 m


As shown in the figure, AX and BY are the two legs at an angle of 60 to the ground. CD and EF are two steps. AR and BS are perpendiculars on the base XY.

AR meets CD at L and EF at P.
BS meets CD at M and EF at Q.
We have, AR = BS = 1.5 m, AB = 0.5 m
AL = LP = PR = BM = MQ = QS = 0.5 m
From right angled ΔAXR,
sin 60=ARAX32=1.5AX AX=1.5×23=33 AX=3 m AX=1.73 mAX=BY=1.73 m

In right angled ΔACL and ΔAEP, ACL=60 and AEP=60
Then ALCL=tan 60 and APEP=tan 60 0.5CL=3 and 1EP=3 CL=0.53 and EP=13 CL=0.5×33 and EP=33
Similarly, MD=0.5×33 and QF=33
Now, CD = CL + LM + MD
=0.5×33+0.5+0.5×33=0.5+33=0.5+1.733
= 0.5 + 0.577 (approx) = 1.077 m

Again, EF=EP+PQ+QF=33+0.5+33=0.5+233=0.5+2×1.733=0.5+3.463=0.5+1.153=1.653m

Hence, and length of step CD = 1.077 m and length of step EF = 1.653 m

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