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

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\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 ( $A,a$ or $B,b$ or $C,c$ ), 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 $A,a$ and $B$ then we could write

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

and solve for $b$ . $C$ could be found from the fact that the angles sum to $180^\circ$ , then write ratios again to solve for $c$ .

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

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

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

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