find m∠w. write your answer as an integer or as a decimal rounded to the nearest tenth. m∠w =
find m∠w. write your answer as an integer or as a decimal rounded to the nearest tenth. m∠w =
Answer
Explanation:
Step1: Apply the cosine - law
The cosine - law for a triangle with sides (a), (b), (c) and the angle (\theta) opposite to side (c) is (c^{2}=a^{2}+b^{2}-2ab\cos\theta). In (\triangle VWX), let (VX = 12), (VW = 9), (WX = 6), and we want to find (\angle W). So, (VX^{2}=VW^{2}+WX^{2}-2\cdot VW\cdot WX\cdot\cos W). Substitute the values: (12^{2}=9^{2}+6^{2}-2\times9\times6\times\cos W).
Step2: Simplify the equation
[ \begin{align*} 144&=81 + 36-108\cos W\ 144&=117-108\cos W\ 108\cos W&=117 - 144\ 108\cos W&=- 27\ \cos W&=-\frac{27}{108}=-\frac{1}{4} \end{align*} ]
Step3: Find the angle
(W=\cos^{-1}(-\frac{1}{4})). Using a calculator, (W\approx104.5^{\circ})
Answer:
(104.5)