c= 5 meters
Explanation
we have a rigth triangle, then
Step 1
Let
[tex]\begin{gathered} \text{angle}=45\text{ \degree} \\ \text{hypotenuse}=5\sqrt[]{2} \\ \text{adjacent side= c} \end{gathered}[/tex]
hence, we need a function that relates: angle, adjacent side and hypotenuse
[tex]\cos \text{ }\emptyset\text{= }\frac{adjacent\text{ side}}{\text{hypotenuse}}[/tex]
now, replace
[tex]\begin{gathered} \cos \text{ }\emptyset\text{= }\frac{adjacent\text{ side}}{\text{hypotenuse}} \\ \cos \text{ 45= }\frac{c}{5\sqrt[]{2}} \end{gathered}[/tex]
Step 2
solve the equation
[tex]\begin{gathered} \cos \text{ 45= }\frac{c}{5\sqrt[]{2}} \\ \frac{\sqrt[]{2}}{2}=\frac{c}{5\sqrt[]{2}} \\ \text{Multiply both sides by 5}\sqrt[]{2} \\ \frac{\sqrt[]{2}}{2}\cdot5\sqrt[]{2}=\frac{c}{5\sqrt[]{2}}\cdot5\sqrt[]{2} \\ \frac{10}{2}=c \\ 5=c \end{gathered}[/tex]
therefore, teh answer is
c=5 meters
I hope this helps you
