#### Answer

$a). 70m$
$b). 0.57min, 0.43min$

#### Work Step by Step

a). Base of the triangle = $50 \times cos37^{\circ}=50\times 0.8=40m$
Thus, the other side = $\sqrt (50^{2}+40^{2})=30m$
So, total distance =$40+30=70m$
b). The student walked around the route for 1 min,
she spent on 40m side for $=\frac{40}{70}\times1=0.57min$
she spent on 30m side for $=\frac{30}{70}\times1=0.43min$