a resultant of two vectors makes 30 degree with one vector and 45 degree with the other. Find the two vectors if the resultant has the magnitude 15

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Let the resultant makes an angle of 30⁰ with vector A such that :
β = 30⁰
θ =75⁰
and R = 15

As the resultant R makes an angle ​β with the direction of vector A.
Hence, tan ​β = $\frac{B \sin \theta }{A + B \cos \theta }$
tan 30⁰ = $\frac{B \sin {75}^0}{A + B \cos {75}^0}$
Solving, we get :
A = 1.41 B    .........(1)
and resultant is given by :
R = $\sqrt{A{ }^2 + B^2 + 2 A B \cos \theta }$
Putting R = 15, A = 1.41 B and θ = 75⁰ in above equation, we get :
B = 7.81 
Substituting value of B in eq. 1, we get :
A = 11.01