Answer
$(a)\space B=6022\space m$
$(b)\space C=6724\space m$
Work Step by Step
Here we use the component method to find B & C.
Since the resultant of the three displacement vectors is zero,
$\vec A+\vec B+\vec C=0$
So, let's set the sum of the x components of the vectors equal to zero.
$A_{x}+B_{x}+C_{x}=0$ ; Let's plug known values into this equation.
$1550\space m\times cos25^{\circ}+Bsin41^{\circ}+(-Ccos35^{\circ})=0$
$C=\frac{1405\space m+0.66B}{0.8}-(1)$
Similarly,
$A_{x}+B_{x}+C_{x}=0$ ; Let's plug known values into this equation.
$1550\space m\times sin25^{\circ}-(+Bcos41^{\circ})+Csin35^{\circ}=0$
$655\space m-0.75B+0.57C=0-(2)$
(1)=>(2)
$655\space m-0.75B+(0.57)\frac{(1405\space m+0.66B)}{0.8}=0$
$524\space m-0.6B+801\space m+0.38B=0$
$B=6022\space m$
(1)=>
$C=\frac{1405\space m+0.66\times6022\space m}{0.8}=6724\space m$
