To find the missing angle measure, we will start by drawing a diagram to illustrate the situation.
We know that the lengths of PN and KP are 21 and 12, respectively. We also know that their included angle has a measure of 67^(∘). To find the measure of ∠ N we need to find KN first. Let's do this one at a time.
Finding KN
With the provided information and using the Law of Cosines, we can write an equation to find p. Then, we will be able to use the Law of Cosines once again for ∠ N.
p^2 = k^2 + n^2 - 2 kn cos P
Let's substitute k= 21, n = 12, and m ∠ P = 67^(∘).
To find m∠ N, we will use the inverse operation of cos, which is cos ^(- 1).
cos N = 685.09/827.4
⇕
m∠ N = cos ^(- 1)(685.09/827.4)
Finally, we will use a calculator.
