Vehicle weight on a slope?

Question

A vehicle needs to winch in a cable with 1000lbs of pressure/weight.

The vehicle weighs 5400lbs

How much of a slope must the vehicle park on to achieve 1000lbs of weight to winch in the cable?

Answer 1

Let $\theta$ be the angle of the slope, then

$$ \sin\theta =\frac{1000}{5400}= \frac{5}{27}$$

Thus, the slope is

$$\tan\theta = \frac{\sin\theta}{\sqrt{1-\sin^2\theta}}=0.19$$