Answer
$$b=40.6m$$
$$c=54.7m$$
Work Step by Step
To find side b, we can use the trigonometric ratio for tangent
$tanA=\frac{a}{b}$
Where
$A=42.1°$
$a=36.7m$
Solving for b we get:
$b=\frac{a}{tanA}$
$b=\frac{36.7m}{tan(42.1°)}$
$b=\frac{36.7m}{0.9036}$
$b=40.6m$
To find side c (the hypotenuse), we can use the trigonometric ratio for sine.
$sinA=\frac{a}{c}$
Where
$A=42.1°$
$a=36.7m$
Solving for c we get:
$c=\frac{a}{sinA}$
$c=\frac{36.7m}{sin(42.1°)}$
$c=\frac{36.7m}{0.6704}$
$c=54.7m$
