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.
Find the sum of all distinct possible values of BC.
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γ=π6=30o
law of sine
sin γ16=sin β15sin 30o16=sin β15sin β=15⋅sin 30o16β=arcsin 15⋅0.516β∈{27.953o,62.047o}
α=180o−30o−{62.047o,27.953o}α∈{87.9532o,122.0468o}
a1sin α1=16sin 30oa1=16⋅sin 87.9532o0.5a1=31.9796
a2sin α2=16sin 30oa2=16⋅sin 122.0468o0.5a2=27.1237
The sum of all distinct possible values of BC is a1+a2=59.1
!