given the triangle, find the length of side $x$ using the law of cosines. round your final answer to 4…
given the triangle, find the length of side $x$ using the law of cosines. round your final answer to 4 decimal places.\n$x = $
Answer
Explanation:
Step1: State the Law of Cosines
$$c^2 = a^2 + b^2 - 2ab \cos(C)$$
Step2: Substitute the given values
$$x^2 = 12^2 + 26^2 - 2(12)(26) \cos(53^\circ)$$
Step3: Calculate the squares and product
$$x^2 = 144 + 676 - 624 \cos(53^\circ)$$
Step4: Evaluate the cosine and simplify
$$x^2 = 820 - 624(0.601815)$$
Step5: Subtract to find $x^2$
$$x^2 = 820 - 375.53256 \approx 444.46744$$
Step6: Take the square root
$$x = \sqrt{444.46744}$$
Answer:
$x = 21.0824$