Question

Find c if a=2.83 mi, b=3.16mi and ∠C=41.2degrees.
Enter c rounded to 3 decimal places.

Answer 1

Check the picture below.

`\textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)\cos(C)\implies c = √(a^2+b^2-(2ab)\cos(C)) \\\\[-0.35em] ~\dotfill\\\\ c = √(2.83^2+3.16^2~-~2(2.83)(3.16)\cos(41.2^o)) \implies c = √( 17.9945 - 17.8856 \cos(41.2^o) ) \\\\\\ c \approx √( 17.9945 - (13.4574) ) \implies c \approx √( 4.5371 ) \implies c \approx 2.130`

Make sure your calculator is in Degree mode.