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Discussion Response Post to: side of triangle

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Priyesh (1601)

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Hi Sanchay

cos(A-B)=31/32

therefore 1-tan^2((A-B)/2)/1+tan^2((A-B)/2)=31/32

by componendo & dividendo 2[[tan^2(A-B)/2)]/2]=(32-31)/(32+31)

or tan^2[(A-B)/2]=1/63

or tan((A-B)/2)=1/sqrt(63) (because A>B)

but tan((A-B)/2)=(a-b)/(a+b) cotC/2 (tangent rule)

this implies

1/sqrt(63)=1/9 * cotC/2therefore we can find the angle C

now we have two side a & b known along with one angle C known

since we know these three paprameters we can find any other angle or side

since we know a, b & angle C

use cosine rule to find side c

Hope you understood

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