Answer:
The surveyor is 36.1 km from the base camp and the base camp is a bearing of 253.4° away.
Explanation:
The diagram of the surveyor's movement is attached to this solution of the problem
From the attached image, the complete motion forms a triangle,
Naming the distance from her base camp x
Using Cosine rule
x² = 42² + 28² - (2×42×28×cos 58°)
x² = 2,548 - 1,246.37 = 1,301.63
x = √1,301.63 = 36.1 km
To obtain the surveyor's bearing from her base camp now, we use sine rule
[(Sin 58°)/x] = [(Sin θ)/42]
Sin θ = (42 × sin 58°)/36.1
θ = sin⁻¹ (0.9866)
θ = 80.6°
Bearing of the surveyor from the base camp = 270° - (80.6° - 64°) = 253.4°
Hope this Helps!!!!