Question

8.12Given the diagram below, what is cos(45") ?450Triangle not drawn to scaleA. 2-3B. 4/2C.D. JE

Answer 1

we have

To find cos 45° we must first find the adjacent and the hypotenuse, so:

let x = adjacent

$\begin{gathered} \tan 45=\frac{opposite}{adjacent} \\ \tan 45=\frac{9}{x} \\ x=\frac{9}{\tan 45} \\ x=9 \end{gathered}$

then find the hypotenuse h:

$\begin{gathered} h^2=9^2+9^2 \\ h^2=81+81 \\ h^2=162 \\ h=\sqrt[]{162} \\ h=9\sqrt[]{2} \end{gathered}$

therefore, cos 45 is:

$\begin{gathered} \cos 45=\frac{adjacent}{hypotenuse} \\ \cos 45=\frac{9}{9\sqrt[]{2}} \\ \cos 45=\frac{1}{\sqrt[]{2}} \end{gathered}$

answer: C