Two sides of a triangle are 5cm and 9cm long.The ratio of the opposite angles is 1:3.Determine the angles and the length of the third side of the triangle!

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Two sides of a triangle are 5cm and 9cm long.The ratio of the opposite angles is 1:3.Determine the angles and the length of the third side of the triangle!

Two sides of a triangle are 5cm and 9cm long.The ratio of the opposite angles is 1:3.Determine the angles and the length of the third side of the triangle!
Two sides of a triangle are 5cm and 9cm long.The ratio of the opposite angles is 1:3.
Determine the angles and the length of the third side of the triangle!

Two sides of a triangle are 5cm and 9cm long.The ratio of the opposite angles is 1:3.Determine the angles and the length of the third side of the triangle!
三角形的两边是5厘米和9厘米长.该两边相对角度比例为1 : 3.确定第三个三角形的一边所对的角度和长度! 设第三变为x,三个角为α,3α,π-4α
由三角面积公式 1/2*5x*sin3α=1/2*5*9sin4α=1/2*9*x*sinα
5sin3α=9sinα 解得sinα=√30/10 第三个角可算得
sinα=√30/10 代入5sin4α=xsinα 得x=4√70/5

三角形有两个边长为5cm和9cm,两边对应的角大小比例为1:3,求三角形的三个角和第三边长度、

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