Solving the triangle F.5
2011-03-22 5:55 am
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In quadrilateral ABCD, B+D=180 ,AB=BC = 4 cm , CD= 6cm and DA=3cm
(1) Prove theat cos B+ cos D=0
(2) Find the length of AC
回答 (1)
2011-03-22 6:10 am
✔ 最佳答案
1)cosB + cosD= cosB + cos(180 - B)= cosB + (- cosB)= 02)cosB = (AB² + BC² - AC²) / (2 AB BC)
cosB = (4² + 4² - AC²) / (2 * 4 * 4)
cosB = (32 - AC²) / 32
;cosD = (AD² + CD² - AC²) / (2 AD CD)
cosD = (3² + 6² - AC²) / (2 * 3 * 6)
cosD = (45 - AC²) / 36By the result of 1) :cosB + cosD = 0(32 - AC²) / 32 + (45 - AC²) / 36 = 09(32 - AC²) + 8(45 - AC²) = 017AC² = 648AC = √(648/17) = 18√34/17 cm
收錄日期: 2021-04-21 22:22:16
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