Answer:
The distance between them after 30 minutes is 6.5 km.
Step-by-step explanation:
Speed = [tex]\frac{distance}{time}[/tex]
Sarah's speed = 6 km/hr = 1.6667 m/s
Emily's speed = 10 km/hr = 2.7778 m/s
The measure of angle between their bearings = [tex]105^{o}[/tex]
After 30 minutes (1800 seconds);
distance = speed x time
Sarah would have covered a distance = 1.6667 x 1800
= 3000 m
= 3 km
Emily would have covered a distance = 2.7778 x 1800
= 5000 m
= 5 km
The distance between them, a, can be determined by applying the cosine rule;
[tex]a^{2}[/tex] = [tex]b^{2}[/tex] + [tex]c^{2}[/tex] - 2bcCos A
= [tex]5000^{2}[/tex] + [tex]3000^{2}[/tex] -2(5000 x 3000) Cos 105
= [tex]5000^{2}[/tex] + [tex]3000^{2}[/tex] -2(5000 x 3000) x (-0.2588)
= 2.5 x [tex]10^{7}[/tex] + 9 x [tex]10^{6}[/tex] + 7764000
= 41764000
a = [tex]\sqrt{41764000}[/tex]
= 6462.5073
a = 6462.5 m
The distance between them after 30 minutes is 6.5 km.
