Starting from one oasis,a camel walks 25 km in a direction 30$\degree$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

The camel walks 25 km in a direction 30° south of west, which means it walks 25 km at an angle of 30° below the west direction. To find the distance between the two oases, we need to find the horizontal component of the camel's walk. The horizontal component is the distance traveled in the west direction, which is 25 km * cos(30°) = 21.65 km. The camel then walks 30 km toward the north, which is perpendicular to the west direction. Therefore, the distance between the two oases is the hypotenuse of a right triangle with legs 21.65 km and 30 km, which is sqrt(21.65^2 + 30^2) = 36.06 km.

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