Question

what is the value of n to the nearest whole number?○ 10○ 13○ 18○ 21law of cosines: $a^{2}=b^{2}+c^{2}-2bc\cos(a)$

Explanation:

Step1: Assign values to cosine law

In $\triangle HNK$, side $n$ is opposite the 90° angle. Let $a=n$, $b=12$, $c=6$, $A=90^\circ$.
Law of cosines: $n^2 = 12^2 + 6^2 - 2(12)(6)\cos(90^\circ)$

Step2: Calculate known terms

$\cos(90^\circ)=0$, so:
$n^2 = 144 + 36 - 2(12)(6)(0)$
$n^2 = 180$

Step3: Solve for n

$n = \sqrt{180} \approx 13.42$

Step4: Round to whole number

Round 13.42 to the nearest whole number.

Answer:

13