$解：?(1)?∵?cos 36°50'=0.8004，??cos 37°=0.7986，??cos A=0.8?$
$∴?36°50'\lt ∠A\lt 37°，??98°\lt ∠ C\lt 98°10'?$
$∴?△ABC?是鈍角三角形$
$? (2) ?如圖，?BD?是邊?AC?上的高，?BD⊥AC，??BD=3，?過點(diǎn)?C?作?CE⊥AB，?垂足為?E?$
$在?Rt △ABD?中，?cos A=\frac {AD}{AB}=\frac {4}{5}?$
$設(shè)?AD=4k，??AB=5k?$
$∴?3^2+(4k)^2=(5k)^2，??k=1?$
$∴?AB=5，??AD=4?$
$在?Rt△ACE?中，?cosA=\frac {AE}{AC}=\frac {4}{5}?$
$設(shè)?AE=4a，??AC=5a?$
$∴?CE=\sqrt{(5a)^2-(4a)^2}=3a?$
$又∵?∠CBE=45°，??∠BEC=90°?$
$∴?BE=CE=3a?$
$∵?BE+AE=AB?$
$∴?3a+4a=5?$
$∴?a=\frac {5}{7}?$
$∴?BE=CE=\frac {15}{7}?$
$∴?BC=\frac {BE}{cos_{45}°}=\frac {15}{7} × \frac {2}{\sqrt 2}=\frac {15\sqrt{2}}{7}?$
