If sinθ = 8/17 and θ is acute; what is the value of sqrt cotθ + tanθ ?

sinθ = \(\frac{8}{17}\),

Therefore, in a right angle triangle:

Perp. = 8, Hypt. = 17 and Base = 15         (Triplet: 8, 15, 17)

So,

⇒ cot θ = \(\frac{base}{perp.}\) = \(\frac{15}{8}\)

⇒ tan θ = \(\frac{perp.}{base}\) = \(\frac{8}{15}\)

and

⇒ cot θ + tan θ = \(\frac{15}{8}\) + \(\frac{8}{15}\)

                         =  \(\frac{225 + 64}{120}\)

                         = \(\frac{289}{120}\)

Therefore,

⇒ \(\sqrt {cot θ + tan θ }\) = \(\sqrt {\frac{289}{120}}\) = \(\frac{17}{2 \sqrt {30 }}\)