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 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 the given triangle, let (a = 11.4) cm, (b=28.4) cm and (\theta = 25.8^{\circ}). We want to find the length of the side opposite the given - angle, say (x). Then (x^{2}=11.4^{2}+28.4^{2}-2\times11.4\times28.4\times\cos(25.8^{\circ})).

Step2: Calculate each term

First, calculate (11.4^{2}=129.96), (28.4^{2}=806.56). (\cos(25.8^{\circ})\approx0.901). (2\times11.4\times28.4\times\cos(25.8^{\circ})=2\times11.4\times28.4\times0.901 = 2\times11.4\times25.5884=582.41792).

Step3: Find (x^{2})

(x^{2}=129.96 + 806.56-582.41792). (x^{2}=936.52-582.41792 = 354.10208).

Step4: Find (x)

(x=\sqrt{354.10208}\approx18.8) cm.

Answer:

(18.8)