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http://chingyihouse.linknethost.com/P1010664.JPGAB is a diameter of the circle centred at O . ABCD is a cyclic quadrilateral . It is given that AD = 15 , CD = 12 and angle ACD = 35 degree(a) Find the radius of the circle(b) Find the length of AC(c) Find the area of quadrilateral ABCD(Give the ans correct... 顯示更多 http://chingyihouse.linknethost.com/P1010664.JPG AB is a diameter of the circle centred at O . ABCD is a cyclic quadrilateral . It is given that AD = 15 , CD = 12 and angle ACD = 35 degree (a) Find the radius of the circle (b) Find the length of AC (c) Find the area of quadrilateral ABCD (Give the ans correct to 3 sig.fig.)

最佳解答:

angle ACB = 90 degree (angle in semicircle) angle BAD = 180 - 90 - 35 = 55 degree In triangle ACD, 12/(sin angle CAD) = 15/(sin 35 degree) angle CAD = 27. 3 degree(corr. to 3 sig. fig.) angle CDA = 180 - 27. 3 - 35 = 117. 7degree (angle sum of triangle) angle BAC = 55 - 27. 3 = 27. 7 degree (b) AC/(sin 117. 7 degree) = 15/(sin 35 degree) AC = 23. 2 (corr. to 3 sig. fig.) (a) AC/BA = cos angleBAC 23. 2/BA = cos 27. 7degree BA = 26. 2 (corr. to 3 sig. fig.) radius = BA/2 = 13. 1 (c) BC = AC tan 27. 7 BC = 12. 2 (corr.to 3 sig. fig.) Area ABCD = triangle ABC + triangle ACD By Heron's formula, Area = 142 + 79. 4 (corr. to 3 sig. fig.) = 221. 4 unit square

其他解答:

• Proverbs
• 數學難題,請計一計
• 請幫我計下喱幾條數

• Proverbs
• 數學難題,請計一計
• 請幫我計下喱幾條數

 

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