Question

In the following diagram, AB is a floor-board; PQRS is a cubical box with each edge = 1 m and ∠B = 60°. Calculate the length of the board AB. 

Answer 1

In ΔPSB, 

`(PS)/(PB) = sin 60^circ`

`=> PB = 2/sqrt(3) = 1.155  m`

In ΔAPQ,

∠APQ = 60°

∴ `(PQ)/(AP) = cos 60^circ`

`=> AP = 1/(1/2) = 2  m`

∴ AB = AP + PB

= 2 + 1.155

= 3.155 m