Question

Starting from one oasis, a camel walks 25 km in a direction 30° south of west and then walks 30 km toward the north to a second oasis. What is the direction from the first oasis to the second oasis?Select one:a.21° N of Wb.39° W of Nc.69° N of Wd.51° W of Ne.42° W of N

Answer 1

To help us determine the direction, let's make an illustration of the problem.

1. 25 km 30°SW

2. 30 km N to the second oasis

To determine the value of x, we can use sine function.

$\sin \theta=\frac{opposite}{\text{hypotenuse}}$

where the opposite side of the angle is 30 - x km while the hypotenuse is 25 km. Let's plug this in to the function above.

$\begin{gathered} \sin 30=\frac{30-x}{25} \\ 25\sin 30=30-x \\ 12.5=30-x \\ x=30-12.5 \\ x=17.5 \end{gathered}$

Using Pythagorean Theorem, let's solve for the value of y.

$\begin{gathered} y=\sqrt[]{(25km)^2-(30km-xkm)^2} \\ y=\sqrt[]{25^2-12.5^2} \\ y=\sqrt[]{625-156.25} \\ y=\sqrt[]{468.75} \\ y=21.6506km \end{gathered}$

To get the angle formed by x = 17.5 km and y = 21.6506km, let's use the tangent function.

$\begin{gathered} \tan \theta=\frac{x}{y} \\ \tan \theta=\frac{17.5}{21.6506} \\ \theta=\tan ^{-1}\frac{17.5}{21.6506} \\ \theta=38.948\approx39NW \end{gathered}$

This means the direction of the oasis is 39° North of West or 51° West of North. The answer is found in Option D.