在三角形ABC中,已知a=2 b=2根号2 c=15° 解此三角形

用余弦定理解 要详解
2024-12-16 17:59:47
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回答1:

a=2,b=2√2,C=15°=π/12
c^2=a^2+b^2-2abcosC
=4+8-2*2*2√2cos(π/12)
=12-8√2cos(π/12)
=12-8√2√{[1+cos(π/6)]/2}
=12-8√[1+√3/2]
=12-8√[(4+2√3)/4]
=12-8[(1+√3)/2]
=12-4(1+√3)
=8-4√3
=2(4-2√3)
=2(2√3-1)^2
=(2√6-√2)^2
c=2√6-√2