find m∠w. write your answer as an integer or as a decimal rounded to the nearest tenth. m∠w = °

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines for finding an angle in a triangle with sides (a), (b), (c) is (\cos C=\frac{a^{2}+b^{2}-c^{2}}{2ab}). In (\triangle WXY), let (a = 8), (b=12), (c = 5), and we want to find (\angle W). So (\cos W=\frac{8^{2}+12^{2}-5^{2}}{2\times8\times12}).

Step2: Calculate the numerator and denominator

First, calculate the numerator: (8^{2}+12^{2}-5^{2}=64 + 144-25=183). Then, calculate the denominator: (2\times8\times12 = 192). So (\cos W=\frac{183}{192}\approx0.953125).

Step3: Find the angle

(W=\cos^{- 1}(0.953125)\approx18.0^{\circ})

Answer:

(18.0)