Solution of Simultaneous Equations

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Here, A, B and C are angles and P,Q,R,S and T are related by the given equations below. We have P=222.5 and Q=445 and given Equation No.s -

1) A+B=90°

2) A-B=2C

3) P=R(cosA) + S(sinC)

4) Q+S(sinC)=T(cosB)

5) S(cosC)=R(sinA)

6) S(cosC)=T(sinB)

Find Angle C, and the values of R,S and T


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From the second equation we get $$C=\frac{A-B}{2}$$ then we get $$Q+S\sin\left(\frac{A-B}{2}\right)=T\cos(B)$$ so $$T=\frac{Q+S\sin\left(\frac{A-B}{2}\right)}{\cos(B)}$$ with this equation we get $S$ from $$S\cos\left(\frac{A-B}{2}\right)=\tan (B)\left(Q+S\sin\left(\frac{A-B}{2}\right)\right)$$ From here we get $S$ and then $T$ and then $R$