Answer:
[tex]Tan(A+B)=\frac{264}{23}[/tex]
Step-by-step explanation:
From the question we are told that:
[tex]SinA=\frac{28}{53}[/tex]
[tex]CosB=\frac{3}{5}[/tex]
Let X be the adjective side to A
Let Y be the opposite side to B
Generally the equation for X is mathematically given by
[tex]X^2=\sqrt{53^2-28^2}[/tex]
[tex]X=45[/tex]
Therefore [tex]TanA[/tex]
[tex]TanA=\frac{28}{45}[/tex]
Generally the equation for Y is mathematically given by
[tex]Y^2=\sqrt{5^2-3^2}[/tex]
[tex]Y=4[/tex]
Therefore [tex]TanB[/tex]
[tex]TanB=\frac{4}{3}[/tex]
Generally the equation for [tex]Tan(A+B)[/tex] is mathematically given by
[tex]Tan(A+B)=\frac{TanA+TanB}{1-TanA*TanB}[/tex]
[tex]Tan(A+B)=\frac{\frac{28}{45}+(\frac{4}{3})}{1-(\frac{28}{45})*(\frac{4}{3})}[/tex]
[tex]Tan(A+B)=\frac{264}{23}[/tex]
