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+f
rom+her+base+camp+and+what+is+her+bearing+from+it?
2 answers:
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:
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!!!!
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