ANSWER
Hypotenuse: 16 ft
Leg: 4 ft
EXPLANATION
Given:
A right angle triangle with only one leg = sqrt(240) feet
Desired Outcomes:
Lengths of the leg and hypotenuse
Declaration of variables
Let x represent the length of leg
Hypotenuse = 4 times the length of leg = 4x
Apply Pythagorean theorem
[tex]\begin{gathered} Hyp^2=Opp^2+Adj^2 \\ (4x)^2=x^2+(\sqrt{240})^2 \\ 16x^2\text{ = }x^2\text{ + 240} \\ 16x^2-x^2\text{ = 240} \\ 15x^2\text{ = 240} \\ x^2\text{ = }\frac{240}{15} \\ x\text{ =}\sqrt{16} \\ x\text{ = 4 ft} \end{gathered}[/tex]Hypotenuse = 4x = 4 (4) = 16 ft
Hence, the Lengths of the leg and hypotenuse are 4 ft and 16 ft respectively.
