Question

a water taxi leaves its dock, and travels 7 km due north to pick up medical supplies. it then travels 15 km due east to drop off the supplies at a hospital. to the nearest degree, what is the measure of the angle between the path it took due east and the path it will take to return directly to its dock?
select one:
a. 62°
b. 28°
c. 25°
d. 65°

Explanation:

Step1: Identify the right - triangle

The water taxi's path forms a right - triangle. The northward distance is one leg ($a = 7$ km) and the eastward distance is the other leg ($b = 15$ km). The return path is the hypotenuse. The angle $\theta$ we want to find is related to the two legs of the right - triangle.

Step2: Use the tangent function

We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. In this case, if the angle $\theta$ is the angle between the east - ward path and the return path, the opposite side to $\theta$ is the northward distance and the adjacent side is the eastward distance. So, $\tan\theta=\frac{7}{15}$.

Step3: Calculate the angle

We find $\theta$ by taking the inverse tangent of $\frac{7}{15}$. $\theta=\arctan(\frac{7}{15})$. Using a calculator, $\theta=\arctan(\frac{7}{15})\approx25^{\circ}$.

Answer:

C. $25^{\circ}$