In the following diagram AB is a floor board. PQRS is a cubical box with edge 1m and angle B is equal to 60 degree. Calculate the length of board AB
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Given - SP = PQ = RQ = RS = 1m
In ΔBSP
Tan60° = SP / BS
√3 = 1 / BS
BS = 1 / √3
In ΔABR
Cos60° = BR / AB
1/2 = 1+1/√3 / AB
AB/2 = √3+1 / √3
AB = 2√3+2 / √3
Rationalise them
AB = 2√3+6 /3
AB = 2( √3+3 ) / 3
∴ The length of AB = 2( √3+3 ) / 3 m
In ΔBSP
Tan60° = SP / BS
√3 = 1 / BS
BS = 1 / √3
In ΔABR
Cos60° = BR / AB
1/2 = 1+1/√3 / AB
AB/2 = √3+1 / √3
AB = 2√3+2 / √3
Rationalise them
AB = 2√3+6 /3
AB = 2( √3+3 ) / 3
∴ The length of AB = 2( √3+3 ) / 3 m
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