Question

Find the length x to the nearest whole number

Answer 1

Check the picture below.

$tan(65^o)=\cfrac{\stackrel{opposite}{310}}{\underset{adjacent}{y}}\implies y=\cfrac{310}{tan(65^o)} \\\\[-0.35em] ~\dotfill\\\\ tan(32^o)=\cfrac{\stackrel{opposite}{310}}{\underset{adjacent}{y+x}}\implies y+x=\cfrac{310}{tan(32^o)}\implies x=\cfrac{310}{tan(32^o)}~~ - ~~y \\\\\\ x=\cfrac{310}{tan(32^o)}~~ - ~~\cfrac{310}{tan(65^o)}\implies x\approx 352$

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