The distance can be determined by applying the cosine rule. Thus the distance back to camp from the second stop is 5.7 km
The appropriate method to determine the distance is by the application of Cosine rule. Let the distance be represented by x.
Thus;
[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2ab Cos C
C = [tex]058^{o}[/tex] + [tex]77^{o}[/tex]
= [tex]135^{o}[/tex]
So that,
[tex]x^{2}[/tex] = [tex]5^{2}[/tex] + [tex]8^{2}[/tex] - 2(5 x 8) Cos [tex]135^{o}[/tex]
= 25 + 64 - 80 (-0.7071)
= 89 - 56.57
[tex]x^{2}[/tex] = 32.43
x = [tex]\sqrt{32.43}[/tex]
= 5.7
x = 5.7 km
Therefore, the distance back to camp from the second stop is 5.7 km.
A sketch for the question is attached to this answer for clear understanding.
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