知道直角三角形的三个度数和一条边的边长,怎样求另外两个边的变长

2025-03-14 21:38:01
推荐回答(1个)
回答1:

使用正弦定理或者余弦定理就可以解决了!
在任意△ABC中,角A、B、C所对的边长分别为a、b、c,三角形外接圆的半径为R。则有:
a/sinA = b/sinB =c/sinC = 2r=R

一个三角形中,各边和所对角的正弦之比相等,且该比值等于该三角形外接圆的直径(半径的2倍)长度。
余弦定理,是描述三角形中三边长度与一个角的余弦值关系的数学定理,是勾股定理在一般三角形情形下的推广。余弦定理是揭示三角形边角关系的重要定理,直接运用它可解决一类已知三角形两边及夹角求第三边或者是已知三个边求角的问题,若对余弦定理加以变形并适当移于其它知识,则使用起来更为方便、灵活。
cos A=(b²+c²-a²)/2bc

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