## anonymous one year ago Will follow and award!!1 Consider a triangle ABC. Suppose that a=31 ,b=57, and c=71 . (The figure is not drawn to scale.) Solve the triangle. Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth. If no such triangle exists, enter "No solution." If there is more than one solution, use the "or" button.

1. mathstudent55

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2. mathstudent55

Since you don't have any angle, you need to use the law of cosines.

3. mathstudent55

Are you familiar with the law of cosines?

4. anonymous

not really

5. mathstudent55

The law of cosines can be written three different ways: $$a^2 = b^2 + c^2 - 2 bc\cos A$$ $$b^2 = a^2 + c^2 - 2 ac\cos B$$ $$c^2 = a^2 + b^2 - 2 ab\cos C$$

6. mathstudent55

Since you have all side lengths, a, b, and c, choose whichever version of the law of cosines above you want to use and solve for the angle in it. Then find the second angle with the law of sines. For the third angle, just subtract the two known angles from 180.

7. anonymous

I got it thanks!