Answer:
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).