Question

A+surveyor+leaves+her+bade+camp+and+drives+42km+on+abearing+of+032°.+She+then+drives+28km+on+a+bearing+of+154°.+How+far+is+she+from+her+base+camp+and+what+is+her+bearing+from+it?

Answer 1

Answer:

36.078km

253.2°

Step-by-step explanation:

Distance from her base camp could be calculated using the cosine rule:

And the angle calculated using the sine rule

AB = c = 42 KM, BC = a = 28 KM, AC = b =?

Answer 2

Answer:

The surveyor is 36.1 km from the base camp and the base camp is a bearing of 253.4° away.

Step-by-step 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!!!!