在三角形ABC中,a=2√2,b=2√3,c=15° 解三角形

2个回答

  • cosC=cos15°

    =cos(45°-30°)

    =cos45°cos30°+sin45°sin30°

    =√2/2×√3/2+√2/2×1/2

    =(√6+√2)/4

    c²=a²+b²-2abcosC

    =(2√2)²+(2√3)²-2×2√2×2√3×(√6+√2)/4

    =8+12-2√6×(√6+√2)

    =20-12-4√3

    =8-4√3

    c=√(8-4√3)

    =2√(2-√3)

    =2√[(4-2√3)/2]

    =2√[(√3-1)²/2]

    =2(√3-1)×√2/2

    =√6-√2

    cosA=(b²+c²-a²)/(2bc)

    =[(2√3)²+(√6-√2)²-(2√2)²]/[2×2√3×(√6-√2)]

    =(12+8-4√3-8)/(12√2-4√6)

    =(12-4√3)/(12√2-4√6)

    =(3-√3)/(3√2-√6)

    =(3-√3)(3√2+√6)/[(3√2+√6)(3√2-√6)]

    =(9√2-3√2)/(18-6)

    =6√2/12

    =√2/2

    A=45°

    B=180°-(A+C)=180°-(45°+15°)=120°