Question

Solve for angles x and y in the triangle below. Round your angle to the nearest whole degree.

Solve for both x and y

Answer 1

`\tan(y )=\cfrac{\stackrel{opposite}{6}}{\underset{adjacent}{4}} \implies \tan( y )= \cfrac{3}{2} \implies \tan^(-1)(~~\tan( y )~~) =\tan^(-1)\left( \cfrac{3}{2} \right) \\\\\\ y =\tan^(-1)\left( \cfrac{3}{2} \right)\implies y \approx 56.31^o \\\\[-0.35em] ~\dotfill\\\\ \tan(x )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{6}} \implies \tan( x )= \cfrac{2}{3} \implies \tan^(-1)(~~\tan( x )~~) =\tan^(-1)\left( \cfrac{2}{3} \right) \\\\\\ x =\tan^(-1)\left( \cfrac{2}{3} \right)\implies x \approx 33.69^o`

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