In △ABC, A and B are acute angles such that sinA = 4/5 and sinB = 8/17.
a). Withough using a calculator, find the value of sinC.
(呢題我搵到架喇... sinC = 84/85)
我不懂的是b題, 即以下的題目
b). If the perimeter of △ABC is 48 cm, find the lengths of the three sides.
唔該幫幫忙~~
一題A Maths 的 Compound Angles 問題
2009-05-25 5:50 am
回答 (2)
2009-05-25 6:11 am
2009-05-25 6:28 am
In △ABC, A and B are acuteangles such that sinA = 4/5 and sinB = 8/17.
a). Withough using acalculator, find the value of sinC.
Sol
sinA=4/5,sinB=8/17=>cosA=3/5,cosB=15/17
SinC=sin(pi-A-B)=sin(A+B)=sinAcosB+sinBcosA
=4/5*15/17+8/17*3/5
=(60+24)/85
=84/85
b). If the perimeter of △ABC is 48 cm, find thelengths of the three sides
Sol
a/sina=b/sinb=c/sinc
a/(4/5)=b/(8/17)=c/(84/85)=(a+b+c)/(4/5+8/17+85/84)
=48/(192/85)=85/4
a=4/5*.85/4=17
b=8/17*85/4=10
c=84/85*85/4=21
a). Withough using acalculator, find the value of sinC.
Sol
sinA=4/5,sinB=8/17=>cosA=3/5,cosB=15/17
SinC=sin(pi-A-B)=sin(A+B)=sinAcosB+sinBcosA
=4/5*15/17+8/17*3/5
=(60+24)/85
=84/85
b). If the perimeter of △ABC is 48 cm, find thelengths of the three sides
Sol
a/sina=b/sinb=c/sinc
a/(4/5)=b/(8/17)=c/(84/85)=(a+b+c)/(4/5+8/17+85/84)
=48/(192/85)=85/4
a=4/5*.85/4=17
b=8/17*85/4=10
c=84/85*85/4=21
收錄日期: 2021-04-22 00:44:24
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090524000051KK02125