Prove the Laws of Sines and Cosines and use them to solve problems.
Select a triangle law and complete the measurement
Problem
\(\text{Two}~\text{landmark}~\text{rays}\) are \(8~\text{km}\) and \(11~\text{km}\) long with an included angle of \(40°\), as shown. Use an appropriate triangle law to find separation \(d\) to the nearest tenth of a kilometer.
Translate the two measured rays and the angle between them into an SAS triangle. The desired separation lies opposite the included angle, so match it to the opposite-side form of the Law of Cosines and take the positive square root. Preserve calculator precision until the requested rounding and retain the context's distance units.
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