Question

what is the value of n to the nearest whole number? law of cosines: a² = b² + c² - 2bccos(a)

Explanation:

Step1: Identify sides and angle

Side HK = n (opposite 90°), HN=20, NK=9, angle N=90°.

Step2: Apply Law of Cosines

$n^2 = 20^2 + 9^2 - 2 \times 20 \times 9 \times \cos(90^\circ)$

Step3: Simplify using cos(90°)=0

$n^2 = 400 + 81 - 0 = 481$

Step4: Solve for n

$n = \sqrt{481} \approx 21.93 \approx 22$

Answer:

B. 22