Question

applying the cosine law
example 2 a nebo svu counter - stealth radar has detected an f - 35 fighter jet at a range of 41 km and is tracking an su - 35s russian fighter jet at 34 km. the angle between the two aircraft is 112°. how far apart are they rounded to nearest tenth?
answer solution

Explanation:

Step1: Recall the cosine - law formula

The cosine - law for a triangle with sides \(a\), \(b\), \(c\) and the angle \(C\) between sides \(a\) and \(b\) is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). Let \(a = 41\), \(b = 34\), and \(C=112^{\circ}\).

Step2: Substitute values into the formula

\[

$$\begin{align*} c^{2}&=41^{2}+34^{2}-2\times41\times34\times\cos(112^{\circ})\\ c^{2}&=1681 + 1156-2788\times(- 0.3746)\\ c^{2}&=1681+1156 + 1044.4848\\ c^{2}&=3881.4848 \end{align*}$$

\]

Step3: Find the value of \(c\)

\[c=\sqrt{3881.4848}\approx62.3\]

Answer:

\(62.3\) km