Question #72004

1 Answer
Jan 14, 2018

#/_C=63^circ#
#a~~12.0365#
#b~~14.4635#

Explanation:

Since the interior angles of a triangle must add up to #180^circ#
#/_A+/_B+/_C=180^circ#
with the given values #/_A=50^circ# and #/_B=67^circ#
#color(white)("XXX")/_C=180^cir-(50^circ+67^circ)=63^circ#

Now that we know the value of all three angles and the length of side #c# we can find the lengths #a# and #b# using the Law of Sines:
#color(white)("XXX")a/(sin(A))=b/(sin(B))=c/(sin(C))#

with the aid of a calculator:
#color(white)("XXX")a=14/(sin(63^circ)) xx sin(50^circ)~~12.0365#
and
#color(white)("XXX")b=14/(sin(63^circ))xxsin(67^circ)~~14.4635#