Question

mcr3u trigonometry assignment t /29

1. two friends, suban and jas, start from the same point but ride their bikes down two different paths. the paths diverge at an angle of 38°. suban rides down his path at 12 km/h, and jas rides down his path at 14 km/h. determine how far apart the two are after riding at their respective speeds for 90 min. 5t

Explanation:

Step1: Calculate the distances each friend rides

• Suban's distance: \(d_{1}=v_{1}t\), where \(v_{1} = 12\space km/h\) and \(t=\frac{90}{60}=1.5\space h\). So \(d_{1}=12\times1.5 = 18\space km\).
• Jas's distance: \(d_{2}=v_{2}t\), where \(v_{2}=14\space km/h\) and \(t = 1.5\space h\). So \(d_{2}=14\times1.5=21\space km\).

Step2: Apply the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). Here, \(a = 18\), \(b = 21\), and \(C = 38^{\circ}\).

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Answer:

The two friends are approximately \(13\space km\) apart.