# A triangle is given with one side equal to 18m (a) and angles laying on this side equal to 48^circ (A) and 37^circ (B). Find the ramaining angle (C) and sides (b and c).

A triangle is given with one side equal to 18m (a) and angles laying on this side equal to ${48}^{\circ }$ (A) and ${37}^{\circ }$ (B). Find the ramaining angle (C) and sides (b and c).
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saiyansruleA
$\mathrm{\angle }C=180-\mathrm{\angle }A-\mathrm{\angle }B$
$=180-37-48$
$={95}^{\circ }$
$\frac{b}{\mathrm{sin}A}=\frac{a}{\mathrm{sin}C}$
$\frac{b}{{\mathrm{sin}37}^{\circ }}=\frac{18}{{\mathrm{sin}95}^{\circ }}$
$b=\frac{18}{{\mathrm{sin}95}^{\circ }}\left({\mathrm{sin}37}^{\circ }\right)$
$\approx 10.87m$
$\frac{c}{\mathrm{sin}B}=\frac{a}{\mathrm{sin}C}$
$c=\frac{18}{{\mathrm{sin}95}^{\circ }}\left({\mathrm{sin}48}^{\circ }\right)$
$\approx 13.43m$