+2446 The length of \(\overline{AC}\) can be found using the law of cosines. The law of cosines relates the remaining side by knowing two sides and its opposite included angle. I think this picture sums it up nicely.
Knowing this information, we can now find the missing length.
| \(c^2=a^2+b^2-2ab\cos C\) | Now, plug in the values we already know in the diagram and solve for the missing side. |
| \(AC^2=1^2+3^2-2(1)(3)\cos40^{\circ}\) | Now, take the principal square root of both sides since the negative answer is nonsensical in the context of geometry. |
| \(AC=\sqrt{1^2+3^2-2(1)(3)\cos40^{\circ}}\approx2.32\) | No units are given in the problem. |
+2446 The length of \(\overline{AC}\) can be found using the law of cosines. The law of cosines relates the remaining side by knowing two sides and its opposite included angle. I think this picture sums it up nicely.
Knowing this information, we can now find the missing length.
| \(c^2=a^2+b^2-2ab\cos C\) | Now, plug in the values we already know in the diagram and solve for the missing side. |
| \(AC^2=1^2+3^2-2(1)(3)\cos40^{\circ}\) | Now, take the principal square root of both sides since the negative answer is nonsensical in the context of geometry. |
| \(AC=\sqrt{1^2+3^2-2(1)(3)\cos40^{\circ}}\approx2.32\) | No units are given in the problem. |
