Given:
a = x ft
b = 40ft
c = 65ft
According to the Pythagorean Theorem, we can find the value of the hypotenuse of a right triangle through the following formula:
[tex]a^2+b^2=c^2[/tex][tex]c=\sqrt[]{a^2+b^2}[/tex]
Given that:
a = side
b = side
c = hypotenuse
With this formula, we can manipulate it ti find the value of a side instead.
[tex]a^2+b^2=c^2[/tex][tex]a^2=c^2-b^2[/tex][tex]a=\sqrt[]{c^2-b^2}[/tex]
Next, we plug in the given values that we have
[tex]a=\sqrt[]{c^2-b^2}[/tex][tex]x=\sqrt[]{(65)^2-(40)^2}[/tex]
[tex]=\sqrt[]{4225-1600}[/tex][tex]=\sqrt[]{2625}[/tex][tex]x=51.235[/tex]
Since the question are asking to round the answer to the nearest tenth, the final answer would be
[tex]x=51.2\text{ ft}[/tex]
