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:
\[

$$\begin{align*} a^{2}&=(23.6)^{2}+(20.4)^{2}-2\times23.6\times20.4\times\cos65^{\circ}\\ a^{2}&=556.96 + 416.16-963.84\times0.422618\\ a^{2}&=556.96 + 416.16-(963.84\times0.422618)\\ a^{2}&=973.12-407.24\\ a^{2}&=565.88 \end{align*}$$

\]

Step2: Solve for a

Take the square - root of both sides to find the value of $a$.
\[a=\sqrt{565.88}\approx23.8\]

Answer:

$a\approx23.8$