Using the data of the problem, we have:
We have a right triangle:
• hypotenuse h = 1,
,
• cathetus x = 5/8,
,
• cathetus y.
Pitagoras Theorem states that:
[tex]h^2=x^2+y^2.[/tex]
Replacing the values above, we have:
[tex]1^2=(\frac{5}{8})^2+y^2\text{.}[/tex]
Solving for y, we get:
[tex]\begin{gathered} y^2=1-(\frac{5}{8})^2, \\ y^2=1-\frac{25}{64}, \\ y^2=\frac{64-25}{64}, \\ y^2=\frac{39}{64}, \\ y=\sqrt[]{\frac{39}{64}}=\frac{\sqrt[]{39}}{8}\text{.} \end{gathered}[/tex]
Answer
[tex]y=\frac{\sqrt[]{39}}{8}[/tex]
