高一数学题目.写过程,谢谢!
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高一数学题目.写过程,谢谢!
![高一数学题目.写过程,谢谢!](/uploads/image/z/8264882-2-2.jpg?t=%E9%AB%98%E4%B8%80%E6%95%B0%E5%AD%A6%E9%A2%98%E7%9B%AE.%E5%86%99%E8%BF%87%E7%A8%8B%2C%E8%B0%A2%E8%B0%A2%21)
(1) B=π/4 AC=2√5 cosC=2√5/5
sinC=√(1-cos²C)=√5/5
sinA=sin[180°-(B+C)]
=sin(B+C)
=sinBcosC+cosBsinC
=√2/2x2√5/5+√2/2x√5/5
=3√10/10
(2) a/sinA=b/sinB
a=bsinA/sinB=2√5x3√10/10/(√2/2)
=6
c=bsinC/sinB=(2√5x√5/5)/(√2/2)
=2√2
AD²=(a/2)²+c²-2(a/2)c cosB
=9+8-3√2x2√2
=5
ad=√5
sinC=√(1-cos²C)=√5/5
sinA=sin[180°-(B+C)]
=sin(B+C)
=sinBcosC+cosBsinC
=√2/2x2√5/5+√2/2x√5/5
=3√10/10
(2) a/sinA=b/sinB
a=bsinA/sinB=2√5x3√10/10/(√2/2)
=6
c=bsinC/sinB=(2√5x√5/5)/(√2/2)
=2√2
AD²=(a/2)²+c²-2(a/2)c cosB
=9+8-3√2x2√2
=5
ad=√5