Question

If `/_ B` and `/_ Q` are acute angles such that `sin B=sin Q.` Then prove that `/_ B=/_ Q.`

Answer 1

`SinB=(AC)/(AB), Sintheta=(PR)/(PQ)`
`(AC)/(AB)=(PR)/(PQ)`
`(AC)/(PR)=(AB)/(PQ)=K=(BC)/(QR)`
`AB^2=AC^2+BC^2`
`K^2PQ^2=K^2PR^2+BC^2`
`BC=sqrt(K^2(PQ^2-PR^2))`
`BC=Ksqrt(PQ^2-PR^2)`
`BC=QRK`
Since 3 co-ordinates are equal ratios CB=CQ