Question

3. Determine the measure of <CAB, to the nearest degree. ​

Answer 1

Check the picture below.

`\cos(CAD )=\cfrac{\stackrel{adjacent}{12}}{\underset{hypotenuse}{16}} \implies \cos( CAD )= \cfrac{3}{4} \\\\\\ \cos^(-1)(\cos( CAD )) =\cos^(-1)\left( \cfrac{3}{4} \right) \implies CAD =\cos^(-1)\left( \cfrac{3}{4} \right)\implies CAD \approx 41.4^o \\\\[-0.35em] ~\dotfill`

`\tan(BAD )=\cfrac{\stackrel{opposite}{8}}{\underset{adjacent}{12}} \implies \tan( BAD )= \cfrac{2}{3} \\\\\\ \tan^(-1)(~~\tan( BAD )~~) =\tan^(-1)\left( \cfrac{2}{3} \right) \implies BAD =\tan^(-1)\left( \cfrac{2}{3} \right) \\\\\\ BAD \approx 33.7^o \\\\[-0.35em] ~\dotfill\\\\ \measuredangle CAB\implies 41.4^o+33.7^0 ~~ \approx ~~ \text{\LARGE 75}^o`

Make sure your calculator is in Degree mode.