Question

find ( mangle w ).

write your answer as an integer or as a decimal rounded to the nearest tenth.
( mangle w=square^{circ} )

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \( y^{2}=x^{2}+z^{2}-2xz\cos Y\). In \(\triangle WXY\), to find \(\angle W\), we use \( XY^{2}=WX^{2}+WY^{2}-2(WX)(WY)\cos\angle W\). Let \( WX = 14\), \( WY=7\), \( XY = 18\). Then \(18^{2}=14^{2}+7^{2}-2\times14\times7\times\cos\angle W\).

Step2: Simplify the equation

Calculate \(18^{2}=324\), \(14^{2}=196\), \(7^{2} = 49\). The equation becomes \(324=196 + 49-196\cos\angle W\). Then \(324=245-196\cos\angle W\). Rearrange to get \(196\cos\angle W=245 - 324\). So \(196\cos\angle W=-79\). Then \(\cos\angle W=\frac{-79}{196}\approx - 0.403\).

Step3: Find the angle

Since \(\angle W=\cos^{-1}(-0.403)\). Using a calculator, \(\angle W\approx113.8^{\circ}\).

Answer:

\(113.8\)