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

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