Use Pythagorean theorem to find the high of the loading dock (x), as it is a leg of the right triangle above:
[tex]\begin{gathered} hypotenuse^2=Leg1^2+Leg2^2 \\ Leg1^2=hypotenuse^2-Leg2^2 \\ Leg1=\sqrt{hypotenuse-Leg2^2} \end{gathered}[/tex][tex]\begin{gathered} Leg1=x \\ Leg2=19ft \\ hypotenuse=20ft \\ \\ x=\sqrt{(20ft)\placeholder{⬚}^2-(19ft)\placeholder{⬚}^2} \\ x=\sqrt{400ft^2-361ft^2} \\ x=\sqrt{39ft^2} \\ x=6.2ft \end{gathered}[/tex]
Then, the high of the loading dock is 6.2 feet
