Problem

For the triangle shown, \(a~=~6\), \(b~=~10\), and included angle \(C~=~60°\). Use the Law of Cosines to find \(c\) in simplified exact form, then give a decimal approximation.

Prompt SAS triangle with a=6, b=10, included angle C=60°, and opposite side c unknown; exact setup, radical, and decimal are withheld.

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What this problem is really about

Keep the Law of Cosines expression exact while matching the included angle with its opposite side. Use exact special-angle values, take the positive square root for a length, and simplify any radical before introducing a decimal. Evaluate the exact result only once, at the end, and then round to the requested precision.

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c²=6²+10²-2·6·10cos(60°)=76, so c=√76=2√19≈8.72.

Use a plus sign: c²=6²+10²+2·6·10cos(60°)=196, so c=14.00.

Stop at c²=76 and report c=76.00.

Give only the rounded value c≈8.7 and omit the requested exact form 2√19.

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For the triangle shown, \(a~=~6\), \(b~=~10\), and included angle \(C~=~60°\). Use the Law of Cosines to find \(c\) in simplified exact form, then give a decimal approximation.

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