Which Law of Sines applies to this?

Determine which Law of Sines applies, then solve the triangle. Please find a, c, and C.

A=65°
B=10°
b= 21.4

Thanks friends.

1 Answer
Douglas K.
Nov 27, 2017

#a ~~ 111.7#
#c ~~ 119.0#
#C = 105^@#

Explanation:

When given two angles and a side, both forms of the Law of Sines apply.

#a/sin(A) = b/sin(B) = c/sin(C)#

AND

#sin(A)/a = sin(B)/b = sin(C)/c#

It is slightly easier to use the first form to find the length of side a:

#a/sin(A) = b/sin(B)#

#a = bsin(A)/sin(B)#

But the other form is no less applicable:

#sin(A)/a = sin(B)/b#

#bsin(A) = asin(B)#

#a = bsin(A)/sin(B)#

Either form gives you the same equation, when you to solve for a particular side or angle:

#a = 21.4sin(65^@)/sin(10^@)#

#a ~~ 111.7#

We can find the #angle C# by subtracting #angle A# and #angle B# from #180^@#:

#C = 180^@- 10^@-65^@#

#C = 105^@#

#b/sin(B) = c/sin(C)#

#c = bsin(C)/sin(B)#

#c = 21.4sin(105^@)/sin(10^@)#

#c ~~ 119.0#

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