Answer
$A=44.90^{\circ}$.
$B=45.10^{\circ}$.
$a=268.6\;m$.
Work Step by Step
The given values are
$b=269.5\;m$
$c=380.5\;m$.
By using trigonometric ratios.
$\frac{b}{c}=\cos{A}$
Isolate $A$.
$A=\cos^{-1}\left(\frac{b}{c} \right )$
Plug all values.
$A=\cos^{-1}\left(\frac{269.5\;m}{380.5\;m} \right )$
By using degree calculator simplify.
$A=44.90^{\circ}$ (rounded value).
In a right angle triangle sum of other two angles is $90^{\circ}$.
$A+B=90^{\circ}$
Isolate $B$.
$B=90^{\circ}-A$
Plug value of $A$.
$B=90^{\circ}-44.90^{\circ}$
Simplify.
$B=45.10^{\circ}$.
By using Pythagorean theorem.
$a=\sqrt{c^2-b^2}$
Plug all values.
$a=\sqrt{(380.5\;m)^2-(269.5\;m)^2}$
Simplify.
$a=\sqrt{144780.5\;m^2-72630.25\;m^2}$
$a=\sqrt{(72150.25\;m^2)}$
$a=268.6\;m$.
