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Danny is 5 years old and weighs 46 pounds. He is sitting on a swing when his sister Stacey pulls him and the swing back horizontally through an angle of = 45.0° and then holds him at static equilibrium. Find the magnitudes of both H and T.

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ajeigbeibraheem

Answer:

H = 46 lbs

T = 65.05 lbs

Step-by-step explanation:

From the given information:

The information shows a right triangle and the solution comes from the bottom leg H and the top T.

So, using the tangent of the trigonometric function;

tan θ = H/46 lbs

tan (45.0°) = H /46 lbs

1 = H /46 lbs

H = 46 lbs

From the top T

T cos θ = W

T cos 45.0° = 46 lbs

T = 46 lbs/cos 45.0°

T = 46 lbs / 0.7071

T = 65.05 lbs

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