Answer
$T=(285N)i^{\wedge}+(705N)j^{\wedge}$
Work Step by Step
As given, the rope makes $22^{\circ}$ with vertical thus it makes $68^{\circ}$ with horizontal.
The force on Tarzan from the vine is because of tension $T$ which can be calculated as
$T=Tcos{\theta}+Tsin{\theta}$
We plugin the known values to obtain:
$T=760cos68^{\circ}i^{\wedge}+760sin68^{\circ}j^{\wedge}$
$T=(285N)i^{\wedge}+(705N)j^{\wedge}$
