# Help with precalc homework?!

May 1, 2018

$C$

#### Explanation:

The cat is $54 k m$ East and $55 k m$ South. Because these distances form a right angle we can use the pythagorean theorem to find the distance: $\sqrt{{\left(54 k m\right)}^{2} + {\left(55 k m\right)}^{2}} \approx 77.1 k m$. We can assume that the angle is very close to 45 degrees because the legs of the right triangle are almost equal, which leaves us $A$ and $C$ as viable answers. Since the cat was left South and East of its home, it must travel the opposite directions, North and West, to get home. Both $A$ and $C$ satisfy these conditions, so we must decide whether it is West of North or North of West. Since the South component is greater than the East, the North must be greater than the West. Therefore, since 44.5 WoN is closer to due north than 44.5 NoW, we know the answer must be $C$.

May 1, 2018

[D] None of these.

#### Explanation:

Imagine the 54km east and 55km south as legs of a right triangle, and the route that the cat took back as the hypotenuse. We need to find the hypotenuse's length, and the angle formed by the hypotenuse and the 54km line segment.

The hypotenuse's length can be acquired from the Pythagorean Theorem. We'll call d the distance, or length of the hypotenuse.

${54}^{2} + {55}^{2} = {d}^{2}$
$5941 = {d}^{2}$
$d \approx 77.1$

Secondly, we need to find the direction, or the angle formed by the hypotenuse and the positive x axis counterclockwise. This measurement should be (in this case) more than 180 degrees. Since neither a, b, nor c provides a direction of over 180 degrees, the answer must be d.