A surveyor leaves her base camp and drives 42km on a bearing of 032degree she then drives 28km on a bearing of 154degree, how far is she from her camp base and what is her bearing from it

The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).

Step-by-step explanation:

The final position of the surveyor is represented by the following vectorial sum:

(1)

And this formula is expanded by definition of vectors in rectangular and polar form:

(1b)

Where:

- Resulting coordinates of the final position of the surveyor with respect to origin, in kilometers.

- Length of each vector, in kilometers.

- Bearing of each vector in standard position, in sexagesimal degrees.

If we know that , , and , then the resulting coordinates of the final position of the surveyor is:

According to this, the resulting vector is locating in the first quadrant. The bearing of the vector is determined by the following definition:

And the distance from the camp is calculated by the Pythagorean Theorem:

The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).