A(1,-2,11) B(4,2,3) C(6,-1,4)三点,求三角形ABC的面积.要思路,
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/16 10:23:32
![A(1,-2,11) B(4,2,3) C(6,-1,4)三点,求三角形ABC的面积.要思路,](/uploads/image/z/3684756-12-6.jpg?t=A%281%2C-2%2C11%29+B%284%2C2%2C3%29+C%286%2C-1%2C4%29%E4%B8%89%E7%82%B9%2C%E6%B1%82%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E7%9A%84%E9%9D%A2%E7%A7%AF.%E8%A6%81%E6%80%9D%E8%B7%AF%2C)
A(1,-2,11) B(4,2,3) C(6,-1,4)三点,求三角形ABC的面积.要思路,
A(1,-2,11) B(4,2,3) C(6,-1,4)三点,求三角形ABC的面积.要思路,
A(1,-2,11) B(4,2,3) C(6,-1,4)三点,求三角形ABC的面积.要思路,
三角形ABC顶点分别为A(1,-2,11),B(4,2,3),C(6,-1,4)
AB=√[(1-4)^2+(-2-2)^2+(11-3)^2]=√89
AC=√[(1-6)^2+(-2+1)^2+(11-4)^2]=√75
BC=√[(4-6)^2+(2+1)^2+(3-4)^2]=√14
所以AC^2+BC^2=75+14=89,AB^2=89
AC^2+BC^2= AB^2
由勾股逆定理得:
∠ACB=90°
所以s△ABC=1/2*AC*BC=1/2*√75*√14=5√42/2