Using the ratio cosine with the length of the adjacent side of angle 45° to find the hypotenuse (y), we have:
[tex]\begin{gathered} \text{cos}(45)=\frac{\text{ adjacent length}}{\text{hypotenuse}} \\ \cos (45)=\frac{13}{y}\text{ (Replacing)} \\ \cos (45)\cdot y=13\text{ (Multiplying by y on both sides of the equation)} \\ y=\frac{13}{\cos (45)}\text{ (Dividing by cos(45) on both sides of the equation)} \\ y=18.38 \\ y=18.4\text{ (Rounding to the nearest tenth)} \end{gathered}[/tex]Using the ratio tangent with the length of the adjacent side of angle 45° to find the opposite length, we have:
[tex]\begin{gathered} \text{tan}(45)=\frac{\text{ Opposite length}}{\text{Adjacent length}} \\ \tan (45)=\frac{x}{13}\text{ (Replacing)} \\ \tan (45)\cdot13=x\text{ (Multiplying on both sides by 13)} \\ 13=x\text{ (Multiplying; tan(45)=1)} \\ x=13 \end{gathered}[/tex]The answers are x=13 and y=18.4
