Question

two ships leave from the same spot. one travels east for 12 miles. the second ship travels southeast for 15 miles. the angle formed between the two paths of the ships is 15 degrees. how far are the two ships from each other after they traveled those distances? 27 miles 21.26 miles 26.77 miles 4.61 miles

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). Let \(a = 12\), \(b=15\), and \(C = 15^{\circ}\).

Step2: Substitute values into the formula

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We know that \(\cos(15^{\circ})=\cos(45^{\circ}-30^{\circ})=\cos45^{\circ}\cos30^{\circ}+\sin45^{\circ}\sin30^{\circ}=\frac{\sqrt{2}}{2}\times\frac{\sqrt{3}}{2}+\frac{\sqrt{2}}{2}\times\frac{1}{2}=\frac{\sqrt{6}+\sqrt{2}}{4}\approx0.9659\)

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Answer:

4.61 miles