Question

Please show work. thank you!​

Answer 1

Answer:

$\large\boxed{h=\dfrac{\sqrt{703}}{2}ft\approx13.26ft}$

Step-by-step explanation:

Look at the picture.

Use the Pythagorean theorem:

$leg^2+leg^2=hypotenuse^2$

We have:

$leg=\dfrac{9}{2}ft\\\\hypotenuse=14ft\\\\leg=h$

Substitute:

$\left(\dfrac{9}{2}\right)^2+h^2=14^2$

$\dfrac{81}{4}+h^2=196$                multiply both sides by 4

$81+4h^2=784$             subtract 81 from both sides

$4h^2=703$            divide both sides by 4

$h^2=\dfrac{703}{4}\to h=\sqrt{\dfrac{703}{4}}\\\\h=\dfrac{\sqrt{703}}{\sqrt4}\\\\h=\dfrac{\sqrt{703}}{2}\\\\h\approx13.26$