a slider crank mechanism is shown in the figure. find the distance between the wrist pin w and the…

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula for a triangle with sides (a), (b), (c) and the included - angle (\theta) is (c^{2}=a^{2}+b^{2}-2ab\cos\theta). In (\triangle CPW), let (a = 10.8), (b = 28.7), and (\theta=26.9^{\circ}). We want to find the length of the side (CW) (let's call it (x)). Then (x^{2}=10.8^{2}+28.7^{2}-2\times10.8\times28.7\times\cos(26.9^{\circ})).

Step2: Calculate each term

First, calculate (10.8^{2}=10.8\times10.8 = 116.64), (28.7^{2}=28.7\times28.7 = 823.69). And (\cos(26.9^{\circ})\approx0.891). Then (2\times10.8\times28.7\times\cos(26.9^{\circ})=2\times10.8\times28.7\times0.891 = 2\times10.8\times25.5717=555.74808).

Step3: Find (x^{2})

(x^{2}=116.64 + 823.69-555.74808=384.58192).

Step4: Find (x)

Take the square - root of (x^{2}), (x=\sqrt{384.58192}\approx19.6).

Answer:

(19.6)