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 distance separates the two oases?
A) 15 km
B) 48 km
C) 28 km
D) 53 km
E) 55 km

Question

Quizplus · Accepted Answer

To solve this, we can break down the camel's journey into components and use the Pythagorean theorem. The camel first walks 25 km in a direction 30° south of west. This can be broken into a westward component and a southward component. The westward component is $25 \cos(30°)$ and the southward component is $25 \sin(30°)$. Then, the camel walks 30 km north, which directly cancels out some of the southward component.The westward component is $25 \cos(30°) = 25 \times \sqrt{3}/2 \approx 21.65$ km.The southward component before walking north is $25 \sin(30°) = 25 \times 1/2 = 12.5$ km.After walking 30 km north, the net southward component is $12.5 - 30 = -17.5$ km, but since we're looking for distance, we'll consider it as 17.5 km northward.Now, we use the Pythagorean theorem to find the distance between the two oases: $\sqrt{(21.65)^2 + (17.5)^2} \approx \sqrt{468.9225 + 306.25} \approx \sqrt{775.1725} \approx 27.84$ km, which rounds to 28 km.

Starting from One Oasis, a Camel Walks 25 Km in a Direction