Question

given a = 65°, a =?, b =?, b = 23.6, c =?, c = 20.4. try it yourself. a²=(b² + c²)-(2bc cos a), a²=(23.6²+20.4²)-(2×23.6×20.4)cos 65°, a² = 973.12 - 462.88, √a²=√510.24 ≈ 22.6 ≈ 23

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is $a^{2}=b^{2}+c^{2}-2bc\cos A$. Given $b = 23.6$, $c=20.4$ and $A = 65^{\circ}$, we substitute these values into the formula:

$$
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$$

Step2: Solve for a

Take the square - root of both sides to find the value of $a$.

$$a=\sqrt{565.88}\approx23.8$$

Answer:

$a\approx23.8$