Question

Use law of cosines to solve for x (use proofs) please helpppp me

Answer 1

`c\approx9.569\text{ units}`

Explanation:

Given two known sides and one angle, the form of the Law of Cosines we'll want to use is
`c=√(a^2+b^2-2ab\cos\gamma)` where
`a=13`,
`b=17`, and
`\gamma=34^\circ`:

`c=√(a^2+b^2-2ab\cos\gamma)\\c=√((13)^2+(17)^2-2(13)(17)\cos34^\circ)\\c=√(169+289-442\cos34^\circ)\\c=√(458-442\cos34^\circ)\\c\approx9.569\text{ units}`

Thus, the missing side is about 9.569 units.