The 20-in. Tube AB can slide a long a horizontal rod. The ends A and B of the tu

Question

The 20-in. Tube AB can slide a long a horizontal rod. The ends A and B of the tube are connected by elastic cords to the fixed points C. For the position corresponding to x = 11 in., determine the angle formed by the two cords, (a) using Eq. (3.32), (b) apply law of cosines to trinagle ABC.

Correct answer is: 26.8 degrees

I will give you the pts if you can clearly explain how to get to that answer

The 20-in. Tube AB can slide a long a horizontal rod. The ends A and B of the tube are connected by elastic cords to the fixed points C. For the position corresponding to x = 11 in., determine the angle formed by the two cords, (a) using Eq. (3.32), (b) apply law of cosines to trinagle ABC. Correct answer is: 26.8 degrees I will give you the pts if you can clearly explain how to get to that answer cos u = PxQx + PyQy + PzQz/PQ

Explanation / Answer

We need to find the slope of both lines first.

Now for 2x - 5y = 7

5y = 2x - 7

==> y = (2/5)x - 7/5

Hence the slope is 2/5

For x + y = 2, y = 2-x, and hence the slope is -1.

Then we use the formula

tan(theta) = (m2 - m1)/(1 + m1m2) where theta is the acute angle between the two lines and m1 and m2 are the slopes of the lines, where m2 > m1.

In our case, m2 = 2/5 and m1 = -1 (note: m2 > m1)

Then tan(theta) = (2/5 - (-1))/(1+(2/5)(-1))

tan(theta) = (7/5)/(3/5)

tan(theta) = 7/3

Theta = tan^-1(7/3)

theta = 63.2 degrees

The angle between the two lines is 90-63.2=26.8 degrees

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