Question

given the triangle, find the length of side x using the law of cosines. round your final answer to 4 decimal places.

Explanation:

Step1: Recall the Law of Cosines

$x^{2}=20^{2}+16^{2}-2\times20\times16\times\cos(58^{\circ})$

Step2: Calculate each term

$20^{2}=400$, $16^{2}=256$, and $2\times20\times16\times\cos(58^{\circ}) = 640\times\cos(58^{\circ})\approx640\times0.529919 = 339.14816$

Step3: Find $x^{2}$

$x^{2}=400 + 256-339.14816=316.85184$

Step4: Solve for $x$

$x=\sqrt{316.85184}\approx17.8003$

Answer:

$17.8003$