Question

find the length of side c.
a triangle abc is shown with a = 13, b = 18, angle c = 43 degrees. c =?
law of cosines: $c^{2}=a^{2}+b^{2}-2abcdotcos c$
round your final answer to the nearest tenth

Explanation:

Step1: Substitute values into formula

Given $a = 13$, $b = 18$, and $C=43^{\circ}$, substitute into $c^{2}=a^{2}+b^{2}-2ab\cos C$.
$c^{2}=13^{2}+18^{2}-2\times13\times18\times\cos(43^{\circ})$

Step2: Calculate each term

$13^{2}=169$, $18^{2}=324$, and $2\times13\times18\times\cos(43^{\circ})\approx2\times13\times18\times0.7314 = 339.972$.
$c^{2}=169 + 324-339.972$

Step3: Simplify right - hand side

$c^{2}=169+324 - 339.972=153.028$

Step4: Solve for c

$c=\sqrt{153.028}\approx12.4$

Answer:

$12.4$