Q. 57

A carpenter makes stools for electricians with a square top of side 0.5 m and at a height of 1.5 m above the ground. Also, each leg is inclined at an angle of 60° to the ground. Find the length of each leg and also the lengths of two steps to be put at equal distances.

Answer :

In the fig let the height of the stool from the ground is 1.5m i.e. AL = BM = 1.5m


In ∆ACL


tan 60° =


√3 =


CL =


= 0.866m


Again in ∆ACL


Sin 60° =


=


AC = = √3m 1.732m



Lengths of steps are GH and EF and steps are put at equal distance such that AP =PR = RL


Now consider ∆AGP and ∆ACL


=


=


GP = 0.2887m


Length of step = GH = GP + PQ + QH = GP + AB + GP (Since QH = GP)


GH = 2GP + AB = 2 × 0.2887 + 0.5 = 1.0774m


Similarly we can say that,


ER = = 0.577m


Length of the step is EF = ER + RS + SF


ER + AB + ER = 2ER + AB


EF = 2× 0.5773 + 0.5 1.6546m


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