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how to derive the formula R=a/2sinA=b/2sinB=c/2sinC

how to derive the formula R=a/2sinA=b/2sinB=c/2sinC

Grade:12th pass

1 Answers

Vikas TU
14149 Points
3 years ago
Dear STudent,
U need to do some constructions here.
In a Circle of Raddi R inscribing a triangle into it,
with sides a,bandc of Triangle ABC.
From the centre draw a perpendicular to the base and let the angle be thetha of the triangle at O.
Then from Pythodorus the relation will held as:
It is evident that sinθ = a/2R. Hence we have R = a/2 sinθ.
And hence, R=a/2sinA=b/2sinB=c/2sinC.
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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