seems like the answer used by cosine or sine formula is different
Shouldn't the answer be the same in no matter situations?
Thanks!
sine and cosine formula produce different answers?
回答 (1)
2015-08-30 12:59 am
Rt-angle laws:
RQ = √(625 - x^2)
RS = √(400 - RQ^2)
= √(400 - 625 + x^2)
= √(x^2 - 225)
PS = PR - RS
= x - √(x^2 - 225)
Cosine law:
PS^2 = 625 + 400 - 2*20*25*cos12
= 1025 - 1000*cos12
= 46.8524
=> PS = 6.84488 = x - √(x^2 - 225)
=> √(x^2 - 225) = x - PS
=> x^2 - 225 = (x - PS)^2 = x^2 - 2*PS*x + PS^2
=> 2*PS*x = PS^2 + 225
=> x = (PS^2 + 225)/(2*PS)
= (46.8524 + 225)/(2*6.84488)
= 19.848
= Answer
RQ = √(625 - x^2)
RS = √(400 - RQ^2)
= √(400 - 625 + x^2)
= √(x^2 - 225)
PS = PR - RS
= x - √(x^2 - 225)
Cosine law:
PS^2 = 625 + 400 - 2*20*25*cos12
= 1025 - 1000*cos12
= 46.8524
=> PS = 6.84488 = x - √(x^2 - 225)
=> √(x^2 - 225) = x - PS
=> x^2 - 225 = (x - PS)^2 = x^2 - 2*PS*x + PS^2
=> 2*PS*x = PS^2 + 225
=> x = (PS^2 + 225)/(2*PS)
= (46.8524 + 225)/(2*6.84488)
= 19.848
= Answer
收錄日期: 2021-04-11 21:11:35
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https://hk.answers.yahoo.com/question/index?qid=20150829090150AACDmmY