Write a short paragraph explaining how the Law of Sines can be used to solve a right triangle.


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Answered 1 year ago
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asinA=bsinB=csinC\dfrac{a }{\sin A } = \dfrac{b }{\sin B } = \dfrac{c }{\sin C }

To use this, we require 3 pieces of information.

One angle/opposite side pair (A,aA,a or B,bB,b or C,cC,c), and one other side or one other angle.

With this we are able to write an equation with two of these ratios and solve for one unknown. For example if we had A,aA,a and BB then we could write

asinA=bsinB\dfrac{a }{\sin A } = \dfrac{b }{\sin B }

and solve for bb. CC could be found from the fact that the angles sum to 180180^\circ, then write ratios again to solve for cc.

Care must be taken when the information is the SSASSA (side-side-angle) case because of the possibility of there being two solutions.

If given 3 angles only (AAAAAA) or 3 sides only (SSSSSS) we would not be able to use this. AAAAAA by itself does not specify a unique triangle and SSSSSS requires the Law of Cosines in the next section.

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