Question

1. find the missing side length. (2 points) triangle with sides 18, 8 and included angle 43°

Explanation:

Step1: Identify the Law of Cosines

We use the Law of Cosines for a triangle with sides $a$, $b$, included angle $C$, and opposite side $c$:
$$c^2 = a^2 + b^2 - 2ab\cos(C)$$
Here, $a=8$, $b=18$, $C=43^\circ$, solve for $c$.

Step2: Substitute values into formula

$$c^2 = 8^2 + 18^2 - 2(8)(18)\cos(43^\circ)$$
Calculate each term:
$8^2=64$, $18^2=324$, $2(8)(18)=288$, $\cos(43^\circ)\approx0.7314$
$$c^2 = 64 + 324 - 288\times0.7314$$

Step3: Compute intermediate results

$$64+324=388$$
$$288\times0.7314\approx210.6432$$
$$c^2 = 388 - 210.6432 = 177.3568$$

Step4: Solve for $c$

$$c = \sqrt{177.3568}\approx13.32$$

Answer:

$\approx13.32$