Question

In △PNW, NW=12, PM=9, and ∠ZWLP=144∘. Find ∠PNW.

a)18∘

b) 36∘

c) 72∘

d) 144 ∘

Answer 1

Using the Law of Sines, we can find that angle PNW in triangle PNW is approximately 36 degrees.

Step-by-step explanation:

To find the measure of angle PNW in triangle PNW, we can use the Law of Sines. We know that NW=12 and PM=9. We also know that angle ZWLP is 144 degrees. Using the Law of Sines, we can set up the equation: sin(PNW)/12 = sin(144)/9. Cross-multiplying gives us: 9*sin(PNW) = 12*sin(144). Dividing both sides by 9 gives us: sin(PNW) = (12*sin(144))/9. Taking the inverse sine of both sides gives us: PNW = sin^(-1)((12*sin(144))/9). Evaluating this expression, we find that PNW ≈ 36 degrees. Therefore, the answer is option b) 36 degrees.