• 2022-06-05
    测得一块三角形土地的两边边长分别为[tex=3.5x1.143]qyqqQGQhPEYdKuODYsFNaQ==[/tex]m和[tex=3.5x1.143]/gx9WDM3d2ZAEVeItJ9/nA==[/tex]m,这两边的夹角为[tex=3.5x1.214]Ld6lmlayn4Kp/xDtMMJOFhtk1cZtzeRiSGde1+l6SF4=[/tex]。试求三角形面积的近似值,并求其绝对误差和相对误差。
  • 解: 设三角形的两边长分别为[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]和[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex],它们的夹角为[tex=0.5x1.0]YCaAGj51cMYuHuypE42enQ==[/tex],则三角形的面积为[tex=5.5x2.357]gagxlIR+ClgoXvli7x7wD63L4g0tDu7/iHBku71L1+Q=[/tex],[tex=5.857x1.357]vExrzTM7rnWp9cibhlDGVrlM7T38UcfMT7uUL0DQ23E=[/tex][tex=11.143x2.786]LiiCHrrPJsHUhWQGo1eq1bAK27XaydQ655+z3A9D6VXoevTjuJtxKKLUIctTatOqx5JXJmJ7WUb/i8EowQBgppvzjSTHPjEknjy7zCxzbmZ8GpKXxb/MQ0KfIJP1ULcjRUuVccIugT3At0Zu0solK4UWCnvK1TLWNoL3QyVXHLz9qLHzW7wBhtmcf0xOx7Wy[/tex][tex=5.143x2.786]M6g2hR9UaUUfePkPxxHDaAUtSDj0TTV68QKi15cchGtvp3ceJFS1JttF6MYuZ/cqiWdH6fYrNQY21SKzP2MUgA==[/tex][tex=5.0x2.786]p9wT9hoBNYszREO4Vwvq7RsQ/bUbZWC3BR78XkW8+KmU53fAOQ9nSp80AVhMmEF2oz0heTMMlxLmYMzrgIORSA==[/tex][tex=5.357x2.786]p9wT9hoBNYszREO4Vwvq7RsQ/bUbZWC3BR78XkW8+KnBxI6nQu2FThkEOFqusNn4T27aQoLdBXTA88ZaDRmDfaHkSvvlLH+rlvF1k5w4/vs=[/tex][tex=6.286x2.357]l7Em1GYM58NDzuZf5GiKFpjglfsFhzsh8MNVJBcaXFvkrJ27SSVS65Ab+YyHqW3y[/tex][tex=6.286x2.357]x2zfWk7A21/RAeMr7YeiwrgI997sPbvHqL6XDXNAtf/sMxizSNLlV2ZTwiLxWsXB[/tex][tex=6.857x2.357]DQFpVTXzv91+oKKgRAPKGgvL+P/tK9Uz9/p/ck6G9lNH59FaVPKV7nIHjwbD3sLj[/tex][tex=5.143x2.357]kYoqg3jWgrRA+4BLF2H4zhkCR4NxhXqxtKUKfIJS+Hbaw9Ye+HHys6fd7crYsib/[/tex][tex=5.214x2.357]x2zfWk7A21/RAeMr7YeiwnXTPtbYSNEHzr311jAVgKM8yIYEGLt4Vl0LW0kB1tga[/tex][tex=5.786x2.357]DQFpVTXzv91+oKKgRAPKGv/MjDb9Ak9TrNDzaPqJUoVC0lGGIsZP+ODHi4vqV9ZD[/tex],便得 [tex=6.0x2.357]YBYsvvEQQEwDY28qSjt/OR0bdF72cdt8IibHuVDhNRpgSaYv5Y7Su3SUI24y2SnH[/tex][tex=5.214x2.357]x2zfWk7A21/RAeMr7YeiwnXTPtbYSNEHzr311jAVgKM8yIYEGLt4Vl0LW0kB1tga[/tex][tex=5.786x2.357]DQFpVTXzv91+oKKgRAPKGv/MjDb9Ak9TrNDzaPqJUoVC0lGGIsZP+ODHi4vqV9ZD[/tex]。当[tex=4.857x1.214]RvAYz6aoelgqoNRGym3gEg==[/tex],[tex=5.571x2.143]iOPDODBO3OkZ97hoEgHm62DS8NbSk0OS90Xe+I1G4PJ2g7I2ZgeRT1mTmyGvPRqE[/tex],[tex=2.857x1.214]iWaWZ/RrRXdeCGT4xM/8LQ==[/tex],[tex=3.5x2.143]zi8/wOO4tr8jSgRkjlrfL7dOSJ5c60QK6rJPCQp0xes=[/tex]时,三角形面积的近似值为[tex=7.714x2.357]42i2SanzmSD8JdpanN2z64ntbroc2vdNv/tbf49BbmcnS2j7FIfZQvn0sr3VFLNxK89UpW0jYGS39ws8nO/HbA==[/tex][tex=5.929x1.571]B7+bVRYlzAtbL0X6BYZcoFZLcB0BdExWmjVjDKG8dJc=[/tex],绝对误差为 [tex=7.714x2.643]mLRyxz1y50pMNb9/qpottX6o/fRH7UzOl36Cukk+R7F0G3FGmHuujPSy7oUIlT1noG3ZiF/ocU6UF6RNnCNxgu2Hquhh8e1AA8pybsgsRtM=[/tex][tex=6.929x2.643]X0HtpmKZgVQw/5RnzG9A7grl0r049gETig34uIyQfX7SQa9IVIvhZmpbS+I7u3Evb/IB6vsa+aUi+Ji6KmxRew==[/tex][tex=8.0x2.357]X0HtpmKZgVQw/5RnzG9A7vzedfBMw/JvMn6FC7do/59LQEGB0uMFsLlPN+jc5bstcnKT4BMcyGiDNLJscQtatRwLflzqABVZ71je4QJjoPE=[/tex][tex=4.929x1.571]sM+6n3/TagYfPtsFdpywY0mHQL+AU1a5oeEtgdmhlAA=[/tex],相对误差为 [tex=2.071x2.429]2vvHNIZKMcptGjqKhaDi/WkSH8UzsAkrNwAGslX0mtI=[/tex][tex=6.643x2.357]TV6jsyGFovUtzV3pTjGFit/NxqmcJ1fh5MhOSwQREUU=[/tex]。

    举一反三

    内容

    • 0

      已知空间三角形的顶点坐标为[tex=1.0x1.214]2Fe5dbSLid0C+D68Q8kHHg==[/tex](0,1,-2),[tex=1.0x1.214]eVKG/l6KyRj55Qp3xeOQRQ==[/tex](4, 1,-3)及[tex=1.0x1.214]iXfyWRMUgBc9cgx58BoZAA==[/tex](6, 2, 5)。试问:①该三角形是否是直角三角形;②该三角形的面积是多少?

    • 1

      在一个三角形中, 观测了[tex=2.0x1.214]s/df2ZE+BhF7kkKI1Rb3ww==[/tex]两角, 中误差 [tex=7.071x1.357]Y3RNV0hcZSc1hkLJGS9xEPpBuKWccyFFzSUV5PgnC+Ji96dFO3CxzkfMZXRpCEL8[/tex], 用两个观测角值计 算另外一个角, 即 [tex=7.714x1.357]bocpBV4IQPb+K8WiucsOYoUBC8JA35YTEtpZRe0xHoM=[/tex], 试求[tex=0.714x1.0]YiLkHgl7MlxE+QjUplQUKA==[/tex]角的中误差 [tex=1.429x1.0]PQBuQ49cr1WYDqWd9XTCZA==[/tex]是多少?

    • 2

      若三角形的三边长是三次方程 [tex=9.429x1.357]x5/xsD96A55X6qsWk8NXLT4fG3A3Kmd+3XHO9dLdS6o=[/tex] 的三个根,试求此三角形的面积 [tex=0.643x1.0]jLbabU9pW65GUKemsNBJWw==[/tex] 和外接圆的半径 [tex=0.786x1.0]AOSTmhvIsOwsdZlGoks7dg==[/tex].

    • 3

      设有直角三角形,测得其两直角边的长分别为[tex=5.071x1.357]48RgqMQ/GLM/h7ipuHVNzilqcdkSDuWqCUEszuLbERU=[/tex]和[tex=5.571x1.357]aEbDgKRbGLG+LlPmyelwrimXNDlIcDPmwtU7KyXANzA=[/tex]。试求利用上述两值来计算斜边长度时的绝对误差。

    • 4

      给定[tex=3.571x1.357]0jgNZNb5KE0SpRQgBt7oQg==[/tex],设x=0是4重插值节点,x=1是单重插值节点试求相应的Hermite插值公式,并估计误差[tex=4.071x1.357]ZHsKcW72rLaSaexOsDovRw==[/tex]