解方程r1/sina2=r2/sina1=R/sin(a1+a2),其中a1+a2=75,R=330
时间: 2024-01-10 20:04:00 浏览: 33
根据三角函数的定义,我们有:
r1/sin(a2) = r2/sin(a1) = R/sin(a1+a2) = R/sin75
因此,我们可以将原方程中的r1/sina2和r2/sina1用R/sin75来表示,得到:
R/sin75 * sin(a1) = r2
R/sin75 * sin(a2) = r1
将这两个式子代入原方程,得到:
R/sin(a1+a2) = R/sin75
化简后得到:
sin(a1+a2) = sin75
根据三角函数的性质,我们知道sin(x) = sin(180-x),因此,方程的解为:
a1+a2 = 75 或 a1+a2 = 180-75 = 105
如果a1+a2=75,则有:
r1/sin(a2) = R/sin75
r2/sin(a1) = R/sin75
代入R=330,得到:
r1 = 330*sin(a2)/sin75
r2 = 330*sin(a1)/sin75
如果a1+a2=105,则有:
r1/sin(a2) = -R/sin75
r2/sin(a1) = R/sin75
代入R=330,得到:
r1 = -330*sin(a2)/sin75
r2 = 330*sin(a1)/sin75
因此,方程的解为:
r1 = 330*sin(a2)/sin75 或 r1 = -330*sin(a2)/sin75
r2 = 330*sin(a1)/sin75
其中a1+a2=75或a1+a2=105。