Question

In ΔVWX, v = 17 inches, w = 63 inches and ∠X=146°. Find the length of x, to the nearest inch.

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\\\\ x = √(17^2+63^2~-~2(17)(63)\cos(146^o)) \implies x = √( 4258 - 2142 \cos(146^o) ) \\\\\\ x\approx √(4258-(-1775.798))\implies x\approx √(6033.798)\implies x\approx 78~in`

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