How do you solve the triangle given #C=145^circ, b=4, c=14#?

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Answer 1 · 2017-02-08T06:28:24

#hatA~=25.57°#
#hatB~=9.43°#
#a~=10.56#

By the Euler Theorem, you know that:

#b/sin hatB=c/sin hatC#

and you can find

#sin hatB=(b sin hatC)/c#

#=(cancel4^2*sin 145°)/cancel14^7=(2*0.57)/7~=0.16#

and #hatB~=9.43°#

Then #hatA=180°-hatB-hatC#

#~=180°-145°-9.43°=25.57#

By the used theorem, it is:

#a/sin hatA=c/sin hatC#

and therefore is

#a=(c*sin hatA)/sin hatC#

# ~=(14*0.43)/0.57=10.56#