Question

Найти Косинус A, треугольник ABC A(3;9) B(0;6) C(4;2)

Answer 1

AB=√[(0-3)²+(6-9)²]=√(9+9)=√18=3√2
BC=√[(4-0)²+(2-6)²]=√(16+16)=√32=4√2
AC=√[(4-3)²+(2-9)²]=√(1+49)=√50=5√2
BC²=AB²+AC²-2*AB*AC*cosA
cosA= (AB²+AC²-BC²)/(2*AB*AC) = (18+50-32)/(2*3√2*5√2) = 36/60=3/5

Answer 2

AB²=(0-3)²+(6-9)²=9+9=18
AB=3√2
BC²=(4-0)²+(2-6)²=16+16=32
BC=4√2
AC²=(4-3)²+(2-9)²=1+49=50
AC=5√2
cosA=(AB²+AC²-BC²)/2AB*AC=(18+50-32)/2*3√2*5√2=36/60=6/10=0,6