A right triangle is given and it is required that you find the unknown length.
Let the length of the unknown be x.
The right triangle is shown below:
Recall the Pythagorean Theorem which states that in a right triangle, the relationship between the lengths of legs a and b and the length of the hypotenuse, c is:
[tex]a^2+b^2=c^2[/tex]
Substitute the side lengths provided into the equation:
[tex]70^2+x^2=74^2[/tex]
Solve the resulting equation for x:
[tex]\begin{gathered} \Rightarrow x^2=74^2-70^2 \\ \Rightarrow x^2=5476-4900=576 \\ \Rightarrow x^2=576 \\ \text{Take square root of both sides:} \\ \Rightarrow x=\sqrt[]{576}=24 \end{gathered}[/tex]
Hence, the required unknown length is 24 ft
