Question

15 km
72°
17 km
x km

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). Here, \(a = 17\), \(b = 15\), and \(C=72^{\circ}\). So, \(x^{2}=17^{2}+15^{2}-2\times17\times15\times\cos72^{\circ}\).

Step2: Calculate each term

First, \(17^{2}=289\), \(15^{2}=225\). Then, \(\cos72^{\circ}\approx0.3090\). So, \(2\times17\times15\times\cos72^{\circ}=2\times17\times15\times0.3090 = 157.59\).

Step3: Compute \(x^{2}\)

\(x^{2}=289 + 225-157.59=356.41\).

Step4: Find \(x\)

Take the square - root of \(x^{2}\). \(x=\sqrt{356.41}\approx18.9\).

Answer:

\(x\approx18.9\)