∵ α,β为锐角,
∴ sinα>0 cosβ>0 sinβ>0
∵ cosα=1/7
∴ sinα=√(1-cos²α)=√(1 - 1/7²)= (4√3)/7
∵ sin(α+β)= sinαcosβ+cosαsinβ
= (4√3)/7cosβ+(1/7)sinβ = (4√3)/7√(1-sin²β) +(1/7)sinβ
即：(4√3)/7√(1-sin²β) +(1/7)sinβ = 5√3/14
(4√3)/7√(1-sin²β) = 5√3/14 -(1/7)sinβ
两边平方
(48/49)(1-sin²β)= 75/196 - (5√3)/49sinβ + (1/49)sin²β
sin²β- (5√3)/49sinβ- 117/196 = 0
(sinβ- (5√3)/98)² = 5808/9604
sinβ- (5√3)/98 = (44√3)/98
sinβ = (49√3)/98 = (√3)/2
β = 60°