Answer:
[tex]\large\boxed{h=\dfrac{\sqrt{703}}{2}ft\approx13.26ft}[/tex]
Step-by-step explanation:
Look at the picture.
Use the Pythagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
We have:
[tex]leg=\dfrac{9}{2}ft\\\\hypotenuse=14ft\\\\leg=h[/tex]
Substitute:
[tex]\left(\dfrac{9}{2}\right)^2+h^2=14^2[/tex]
[tex]\dfrac{81}{4}+h^2=196[/tex] multiply both sides by 4
[tex]81+4h^2=784[/tex] subtract 81 from both sides
[tex]4h^2=703[/tex] divide both sides by 4
[tex]h^2=\dfrac{703}{4}\to h=\sqrt{\dfrac{703}{4}}\\\\h=\dfrac{\sqrt{703}}{\sqrt4}\\\\h=\dfrac{\sqrt{703}}{2}\\\\h\approx13.26[/tex]
