Answer
The component of Tom's weight that is parallel to the ladder is 566 N
The component of Tom's weight that is perpendicular to the ladder is 376 N
Work Step by Step
We can find the angle $\theta$ that the ladder makes with the vertical.
$cos(\theta) = \frac{2.5~m}{3.0~m}$
$\theta = arccos(\frac{2.5~m}{3.0~m})$
$\theta = 33.6^{\circ}$
We can find the component of Tom's weight $w$ that is parallel to the ladder.
$w_{par}= w~cos(\theta)$
$w_{par}= (680~N)~cos(33.6^{\circ})$
$w_{par}= 566~N$
The component of Tom's weight that is parallel to the ladder is 566 N
We can find the component of Tom's weight $w$ that is perpendicular to the ladder.
$w_{perp} = w~sin(\theta)$
$w_{perp} = (680~N)~sin(33.6^{\circ})$
$w_{perp} = 376~N$
The component of Tom's weight that is perpendicular to the ladder is 376 N
