Practicing Success
If sinθ = \(\frac{8}{17}\) and θ is acute; what is the value of \(\sqrt {cotθ + tanθ }\) ? |
\(\frac{17}{2\sqrt {30 }}\) \(\frac{13}{5\sqrt {15}}\) \(\frac{16}{15}\) \(\frac{17}{5\sqrt {8}}\) |
\(\frac{17}{2\sqrt {30 }}\) |
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, ⇒ \(\sqrt {cot θ + tan θ }\) = \(\sqrt {\frac{289}{120}}\) = \(\frac{17}{2 \sqrt {30 }}\) |