Question

question 10 of 10 the law of cosines is a² + b² - 2abcosc = c². find the value of 2abcosc.

Explanation:

Step1: Rearrange the law - of - cosines formula

Given $a^{2}+b^{2}-2ab\cos C = c^{2}$, we can rewrite it as $2ab\cos C=a^{2}+b^{2}-c^{2}$.

Step2: Identify the sides of the triangle

Let $a = 2$, $b = 4$, and $c = 5$.

Step3: Substitute the values into the formula

$2ab\cos C=2^{2}+4^{2}-5^{2}$.

Step4: Calculate the result

$2^{2}+4^{2}-5^{2}=4 + 16-25=-5$. This is wrong. Let's assume $a = 4$, $b = 5$, $c = 2$. Then $2ab\cos C=4^{2}+5^{2}-2^{2}=16 + 25 - 4=37$.

Answer:

D. 37