Question

If sin A = 3/5 and cos B = 20/29 and angles A and B are in Quadrant 1, find the valueof tan(A + B).

Answer 1

Our approach is to use SOHCAHTOA to derive values for sine and cosines of both A and B.

`\begin{gathered} \sin A=(3)/(5),\text{ cosA=}\frac{\sqrt[]{5^2-3^2}}{5}=(4)/(5) \\ \cos B=(20)/(29),\text{ sinB=}\frac{\sqrt[]{29^2-20^2}}{29}=(21)/(29) \end{gathered}`
`\begin{gathered} \tan (A+B)=\frac{\tan A+\tan B}{1-\text{tanAtanB}}\text{ WHERE} \\ \tan A=(\sin A)/(\cos A),\tan B=(\sin B)/(\cos B) \end{gathered}`
`\begin{gathered} \tan (A+B)=(((3)/(5))/((4)/(5))+((21)/(29))/((20)/(29)))/(1-((3)/(5))/((4)/(5))*((21)/(29))/((20)/(29)))=((3)/(4)+(21)/(20))/(1-(3)/(4)*(21)/(20))=((9)/(5))/(1-(63)/(80))=((9)/(5))/((17)/(80)) \\ \tan (A+B)=8.47 \end{gathered}`

tan (A+B) = 8.47