Question

Help with number 8b pls

"find cot of theta

hypotenuse = 8√5
Adjacent side = 16"

Answer 1

`\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies √(c^2 - a^2)=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{(8√(5))^2 - 16^2}=b\implies \sqrt{8^2√(5^2)-256}=b\implies √(64(5)-256)=b \\\\\\ √(320-256)=b\implies √(64)=b\implies 8=b \\\\[-0.35em] ~\dotfill\\\\ cot(\theta )=\cfrac{\stackrel{adjacent}{16}}{\underset{opposite}{8}}\implies {\Large \begin{array}{llll} cot(\theta )=2 \end{array}}`