Предмет: Геометрия, автор: 4emzan9t

дан треугольник ABC со сторонами AB=34,BC=93,AC=65.
На стороне BC точка M, причем АМ=20. Найдите площадь треугольника AMB.

Ответы

Автор ответа: Матов

Обозначим $BM=x; MC=y$ . $93^2=34^2+65^2-2*34*65*cosBAC\ cosBAC=-frac{817}{1105}$ .
По теореме косинусов получим
$b=BAC\ y=93-x\\ x^2=34^2+20^2-2*34*20*cosb\ y^2=20^2+65^2-2*20*65*cos(arccosfrac{-817}{1105}-b)\$
решим данную систему получим
$x=18; \ x=42$
1) при $x=18\$ площадь по Формуле Герона равна $144$
2) при $x=42$ площадь по Формуле Герона равна $336$

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