Question

a boat traveled north for 28 miles, then turned ( x^circ ) southwest and traveled for 25 miles before stopping. when it stopped, the boat was 18 miles from its starting point. by how many degrees did the direction of the boat change when it made its first turn? round to the nearest degree. 30 degrees 39 degrees 46 degrees 50 degrees law of cosines: ( a^2 = b^2 + c^2 - 2bccos(a) )

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(a^{2}=b^{2}+c^{2}-2bc\cos(A)\). Let \(a = 18\), \(b = 28\), \(c = 25\). Then \(18^{2}=28^{2}+25^{2}-2\times28\times25\times\cos(x)\).

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Step2: Find the angle \(x\)

\(x=\cos^{-1}(0.775)\approx39^{\circ}\)

Answer:

39 degrees