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In triangle ABC, angle BCA = pi/6, AB = 16, and AC = 15 

 

Find the sum of all distinct possible values of  BC.  If there are no possible values, enter 0.

 Feb 7, 2022
 #1
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Find the sum of all distinct possible values of  BC.

 

Hello Guest!

 

γ=π6=30o

law of sine

sin γ16=sin β15sin 30o16=sin β15sin β=15sin 30o16β=arcsin 150.516β{27.953o,62.047o}

α=180o30o{62.047o,27.953o}α{87.9532o,122.0468o}

a1sin α1=16sin 30oa1=16sin 87.9532o0.5a1=31.9796

a2sin α2=16sin 30oa2=16sin 122.0468o0.5a2=27.1237

 

The sum of all distinct possible values of BC is a1+a2=59.1

laugh  !

 Feb 8, 2022

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