## purplemexican one year ago Find all solutions for a triangle with A=30° a=4 b=8

1. mathstudent55

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2. mathstudent55

Law of sines: $$\large \dfrac{4}{\sin 30^o} = \dfrac{8}{\sin B}$$ $$4 \sin B = 8 \sin 30^o$$ $$\sin B = \dfrac{8 \sin 30^o}{4}$$ $$\sin B = 1$$ $$B = 90^o$$ $$C = 180 - 30^o - 90^o = 60^o$$ This means our drawing above is incorrect, ans we have a 30-60-90 triangle.

3. mathstudent55

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4. mathstudent55

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5. mathstudent55

Law of sines: $$\large \dfrac{4}{\sin 30^o} = \dfrac{c}{\sin 60^o}$$ $$\large c = \dfrac{4 \sin 60^o}{\sin 30^o}$$ $$\large c = 6.93$$ Of course, we could have solved for c using the ratio of the lengths of the sides of a 30-60-90 triangle. $$1 : \sqrt 3 : 2$$ $$4 : c : 2$$ $$\dfrac{1}{\sqrt 3} = \dfrac{4}{c}$$ $$c = 4 \sqrt 3 \approx 6.93$$

6. Purplemexican

thank you

7. mathstudent55

You're welcome.