ABC, AB=3, BC=5, cos B= -1/15. Найдите AC

Question

ABC, AB=3, BC=5, cos B= -1/15. Найдите AC

Answer 1

По теореме косинусов
АС²=АВ²+ВС²-2АВ·ВС·соsβ=3²+5²-2·3·5·cos(-1/15)=9+25-30cos(1/15)=34-30cos(1/15)
AC=√(34-30cos(1/15))