Answer:
tan β = [tex]\frac{7}{24}[/tex]
Step-by-step explanation:
Using the identities
sin x = [tex]\frac{1}{cscx}[/tex] , cos x = [tex]\frac{1}{secx}[/tex] , tan x = [tex]\frac{sinx}{cosx}[/tex] , then
sinβ = [tex]\frac{1}{\frac{25}{7} }[/tex] = [tex]\frac{7}{25}[/tex]
cos β = [tex]\frac{1}{\frac{25}{24} }[/tex] = [tex]\frac{24}{25}[/tex]
Then
tan β = [tex]\frac{\frac{7}{25} }{\frac{24}{25} }[/tex] = [tex]\frac{7}{25}[/tex] × [tex]\frac{25}{24}[/tex] = [tex]\frac{7}{24}[/tex]
