Answer
$x=32.3\;ft$.
$A=58.2^{\circ}$.
Work Step by Step
In the figure Illustration 3 is a right angle triangle.
Where, given values are
Hypotenuse $c=38.0\;ft$.
one leg $a=20.0\;ft$.
other leg $b=x$.
By using Pythagorean theorem.
$c^2=a^2+b^2$
Plug all values.
$(38.0\;ft)^2=(20.0\;ft)^2+x^2$
Isolate $x$.
$x=\sqrt{(38.0\;ft)^2-(20.0\;ft)^2}$
Simplify.
$x=\sqrt{(1444\;ft^2-400\;ft^2}$
$x=\sqrt{(1044\;ft^2}$
$x=32.3\;ft$.
By using trigonometric ratios.
$\cos{A}=\frac{20.0\;ft}{38.0\;ft}$
Isolate $A$.
${A}=\cos^{-1}\left(\frac{20.0\;ft}{38.0\;ft} \right )$
Simplfiy.
$A=58.2^{\circ}$.
