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A.maths 高手請答~!
發問:
1. In triangle ABC ,A& B are acute angles such that sinA=4/5 sin B =8/17 (a) without using a calculator ,find the value of sinC. (b) If the perimeter of triangle ABC is 48 cm, find the lengths of the three sides.
最佳解答:
(a) 圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Maths/Crazytrigo78.jpg (b) 圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Maths/Crazytrigo79.jpg
1.(a) ∵cosA=√(5^2-4^2)/5=3/5 cosB=√(17^2-8^2)/17=15/17 ∴sinC =sin(180-A-B) =sin(A+B) =sinAcosB+cosAsinB =(4/5)(15/17)+(3/5)(8/17) =84/85 1.(b) ∵a/sinA=b/sinB=c/sinC=2R sinA:sinB:sinC=a/2R:b/2R:c/2R=a:b:c 而sinA:sinB:sinC=4/5:8/17:84/85=68:40:84=a:b:c 設a=68k,b=40k,c=84k 即a+b+c=68k+40k+84k=48 192k=48 k=1/4 ∴a=17cm,b=10cm,c=21cm
A.maths 高手請答~!
發問:
1. In triangle ABC ,A& B are acute angles such that sinA=4/5 sin B =8/17 (a) without using a calculator ,find the value of sinC. (b) If the perimeter of triangle ABC is 48 cm, find the lengths of the three sides.
最佳解答:
(a) 圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Maths/Crazytrigo78.jpg (b) 圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Maths/Crazytrigo79.jpg
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其他解答:1.(a) ∵cosA=√(5^2-4^2)/5=3/5 cosB=√(17^2-8^2)/17=15/17 ∴sinC =sin(180-A-B) =sin(A+B) =sinAcosB+cosAsinB =(4/5)(15/17)+(3/5)(8/17) =84/85 1.(b) ∵a/sinA=b/sinB=c/sinC=2R sinA:sinB:sinC=a/2R:b/2R:c/2R=a:b:c 而sinA:sinB:sinC=4/5:8/17:84/85=68:40:84=a:b:c 設a=68k,b=40k,c=84k 即a+b+c=68k+40k+84k=48 192k=48 k=1/4 ∴a=17cm,b=10cm,c=21cm
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