Problem

In the triangle shown, \(a~=~5,~b~=~6,~\text{and}~c~=~7\) is opposite \(C\). Use the Law of Cosines to find angle \(C\) to \(\text{one}~\text{decimal}~\text{place}\).

Prompt SSS triangle with sides a=5, b=6, and c=7, where c is opposite unknown angle C; the Law of Cosines setup and result are withheld.

Big Picture

What this problem is really about

When all three sides are known, first identify which side is opposite the requested angle. Rearrange the Law of Cosines to isolate that angle's cosine, simplify the exact ratio, and then apply inverse cosine in degree mode. Round only the final angle and check that larger sides face larger angles.

Answer choices

Choose your path.

Preview only

Omit the factor 2: cos(C)=(5²+6²-7²)/(5·6)=0.4, so C=66.4°.

cos(C)=(5²+6²-7²)/(2·5·6)=1/5, so C=arccos(1/5)=78.5°.

Compute arccos(1/5)=1.369 radians but report that as C=1.4°.

Reverse the numerator signs: cos(C)=(7²-5²-6²)/(2·5·6)=-1/5, so C=101.5°.

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

In the triangle shown, \(a~=~5,~b~=~6,~\text{and}~c~=~7\) is opposite \(C\). Use the Law of Cosines to find angle \(C\) to \(\text{one}~\text{decimal}~\text{place}\).

What this problem is really about

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.