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

Explanation / Answer

C = 0 i + 24 j -12 k

A = 11i + 0 j + 0 k

B = 31 i + 0 j + 0 k

AC = A - C = 11 i -24 j + 12 k

BC = B - C = 31 i - 24 j + 12 k

Angle between AC and AB

cos theta =( AC . BC) / | AC| * | BC |

AC . BC = 11* 31 +24 * 24 + 12 *12 = 1061

| AC| * | BC | = sqrt( 11^2 +24^2 +12^2 ) * sqrt( 31^2 +12^2 +24^2) = 1189

cos theta = 1061/1189

theta = cos^-1 (1061/1189) = 26.83 degrees

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