郭敦顒回答:
∵sina+[sina/√(1-sin^2a)]=1
∴ [sina/√(1-sin^2a)]=1-sina,
两边平方得,sin²a/(1-sin²a)=1-2sina+sin²a,
sin²a=(1+sin²a)(1-sin²a) -2sina(1-sin²a),
sin²a=(1-sin^4a) -2sina+2sin³a,
sin^4a-2sin³a + sin²a+2sina-1=0,
解这个4次方程得,
sina≈0.4689899435,
∠A=27.9687515°;
∵(1-sin^2a)= cos²a,∴[sina/√(1-sin^2a)]= sina/cosa= tana,
∴sina+ tana=1,
用尝试——逐步逼近法解得,
sina≈0.4689899435,tana≈0 .5310100565,
∠A=27.9687515°.