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.
Let the length of stool,AB = 0.5 m, height AC = 1.5 m and its leg inclined at an angle of 60° to the ground.
Let the length of leg AE = hm
We have to find the length of leg, lengths of two steps equal in length.
in ΔAEC, ∠AEC = 60°
`sin 60° = (AC)/(AE)`
`=> sqrt3/2 = 1.5/h`
`=> h = 3/sqrt3`
=> h = 1.732
In ΔAGH, ∠AGH = 60° and AH = 0.5 m
`tan 60^@ = (AH)/(GH)`
`=> sqrt3 = 0.5/GH`
`=> GH = 0.5/sqrt3`
`=> GH = 0.2886`
Total length = `0.5 + (0.2886 xx 2) = 1.1077 m`
In Δ APQ, ∠APQ = 60° and AQ = 1 m
`tan 60^@ = (AQ)/(PQ)`
`=> sqrt3 = 1/Pq`
`=> PQ = 1/sqrt3`
=> PQ = 0.577
Total lengths 0.5 + (0.577 x 2) = 1.654 m
Hence the length of leg is 1.732 m
And length of eacb are 1.1077 m and 1.654 m