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# Law of Sines

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if side a is 4 and side b is 3, how long is side c if angle A is 36 degrees?
nielle96  Apr 30, 2012
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#1
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You can always use pythagorean theorem as a shortcut.
EisenhowerStudent  Apr 30, 2012
#2
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a/sin(A) = b/ sin(B) = c/sin(C)

a given.
A given.
b given.
B unknown.

a/sin(A) = b/ sin(B)
sin(B)*a/sin(A) = b
sin(B) = sin(A)*b/a
B = asin( sin(A)*b/a )

c given.
C unknown.

A+B+C = 180
C=180-A-B
C=180-36-asin( sin(A)*b/a )

a/sin(A) = c/sin(C)
sin(C)*a/sin(A) = c
c = sin(C)*a/sin(A)

[input]a=4; b=3; A=36; c = sin( 180-36-asin( sin(A)*b/a ) ) * a / sin( A )[/input]
#3
+3071
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EisenhowerStudent:

You can always use pythagorean theorem as a shortcut.

well, the triangle might not have a 90° angle...

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