missing side is [tex]x} = 12.53[/tex] mi .
Step-by-step explanation:
Here we have the following info from the figure: A right angled triangle with following dimensions
[tex]Perpendicular = x[/tex]
[tex]base = 10[/tex]
[tex]Hypotenuse = \sqrt{257}[/tex]
By Pythagoras Theorem :
[tex]Hypotenuse^2 = Perpendicular^2 + base^2[/tex]
⇒ [tex]Hypotenuse^2 = Perpendicular^2 + base^2[/tex]
⇒ [tex](\sqrt{257})^2 = x^2 + 10^2[/tex]
⇒ [tex]257 = x^2 + 100[/tex]
⇒ [tex]x^2 = 257-100[/tex]
⇒ [tex]x^2 = 157[/tex]
⇒ [tex](x^2)^\frac{1}{2} = (157)^\frac{1}{2}[/tex]
⇒ [tex]x} = (157)^\frac{1}{2}[/tex]
⇒ [tex]x} = 12.53[/tex]
Therefore, missing side is [tex]x} = 12.53[/tex] mi .
