Question

find the length of side c.
a = 47
c = ?
73°
b = 45
law of cosines: c² = a² + b² - 2ab·cosc
round your final answer to the nearest tenth.

Explanation:

Step1: Substitute values into cosine - law formula

Given $a = 47$, $b = 45$, and $C=73^{\circ}$. The law of cosines is $c^{2}=a^{2}+b^{2}-2ab\cos C$. Substitute the values:
\[

$$\begin{align*} c^{2}&=47^{2}+ 45^{2}-2\times47\times45\times\cos(73^{\circ})\\ c^{2}&=2209 + 2025-4230\times\cos(73^{\circ}) \end{align*}$$

\]
We know that $\cos(73^{\circ})\approx0.2924$.
\[

$$\begin{align*} c^{2}&=2209+2025 - 4230\times0.2924\\ c^{2}&=2209 + 2025-1236.852\\ c^{2}&=4234-1236.852\\ c^{2}&=2997.148 \end{align*}$$

\]

Step2: Solve for $c$

Take the square - root of both sides: $c=\sqrt{2997.148}\approx54.7$.

Answer:

$54.7$