Question

NO LINKS!! URGENT HELP PLEASE!!

Use the laws of sines and cosines for the missing variable ​

Answer 1

x = 8

Explanation:

The given diagram shows a triangle with the length of two sides and its included angle.

To find the value of the missing variable x, we can use the Law of Cosines.

`\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}`

From inspection of the given triangle:

• a = 18
• b = 21
• c = x
• C = 22°

Substitute the values into the formula and solve for x:

`\begin{aligned}x^2&=18^2+21^2-2(18)(21)\cos 22^(\circ)\\x^2&=324+441-756\cos 22^(\circ)\\x^2&=765-756\cos 22^(\circ)\\x&=\sqrt{765-756\cos 22^(\circ)}\\x&=8.00306228...\\x&=8\end{aligned}`

Therefore, the value of the missing variable x is x = 8, rounded to the nearest hundredth.