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 angle (\theta) opposite to side (c) is (c^{2}=a^{2}+b^{2}-2ab\cos\theta). In (\triangle CPW), let (a = 10.2), (b=28.3), and (\theta = 24.2^{\circ}). We want to find the length of the side (CW), which we'll call (x). So (x^{2}=10.2^{2}+28.3^{2}-2\times10.2\times28.3\times\cos(24.2^{\circ})).

Step2: Calculate each part

First, calculate (10.2^{2}=104.04), (28.3^{2}=800.89). Then, (\cos(24.2^{\circ})\approx0.911). And (2\times10.2\times28.3\times0.911 = 2\times10.2\times25.7813= 2\times262.96926 = 525.93852).

Step3: Find (x^{2})

(x^{2}=104.04 + 800.89-525.93852=379.00148).

Step4: Find (x)

Take the square - root of (x^{2}), (x=\sqrt{379.00148}\approx19.5).

Answer:

(19.5)