Answer
$d = 3.454~m$
Work Step by Step
We can convert angle $\alpha$ to degrees:
$\alpha = 37'48''$
$\alpha = (\frac{37}{60}+\frac{48}{3600})^{\circ}$
$\alpha = 0.63^{\circ}$
We can convert angle $\beta$ to degrees:
$\beta = 42'03''$
$\beta = (\frac{42}{60}+\frac{3}{3600})^{\circ}$
$\beta = 0.7008^{\circ}$
It is given that $b = 2.000~cm$
We can use the expression for the distance $d$ in part (a) to find the distance $d$ from point P to point Q:
$d = \frac{b}{2~tan(\frac{\alpha}{2})}+\frac{b}{2~tan(\frac{\beta}{2})}$
$d = \frac{2.000~cm}{2~tan(\frac{0.63^{\circ}}{2})}+\frac{2.000~cm}{2~tan(\frac{0.7008^{\circ}}{2})}$
$d = 181.8895~cm+163.5133~cm$
$d = 3.454~m$
