How Far is the Camel From Oasis B?

The distance between Oasis A and Oasis B is 25 km due east. Starting from Oasis A, the camel walks 24 km in a direction 19° south of east and then walks 4.0 km due north.

To find the distance from the camel to Oasis B, we can calculate the vector that goes from A to 15 km east (vector C). By finding the difference between A + B and C (D), we can determine the distance.

Calculating the Distance:

First, we find the components of vectors Ax, Ay, Bx, By:

Ax = 24 cos(15) = 23.1822

Ay = 24 sin(15) = 6.2117

Bx = 0

By = 8

Finding the Difference D:

Using the formula D = (A + B) - C:

Dx = (Ax + Bx) - Cx = 1.8178

Dy = (Ay + By) - Cy = 1.7883

Therefore, the distance D from the camel to Oasis B is approximately 2.2567 km.