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In an Delta ABC as showin in Fig. 2 . (2...

In an `Delta ABC` as showin in Fig. 2 . (2) .71 (a) prove
that ` a/(sin A) =b/(sin B) =C/(sin C)`.

Text Solution

Verified by Experts

From polygon law of vector addition we can see `AB+BC +CA = 0`
`:. chati+(a sin Bhatj - a cos Bhati)`
`+(-b cos Ahati - b sin Ahatj) = 0`
`:. (c-a cos B -b cos A)hati`
`+ (a sin B -b sin A) hatj = 0`

Putting coefficient of `hatj = 0`, we find that,
`(a)/(sin A) = (b)/(sin B)`
Now taking `B` as origin and `BC` as the x-axis, we can
prove other relation.
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