How much force must be produced by the fibers of a pennate muscle aligned at 75°  to a central tendon to create a tensile force of 400 N in the tendon?

To solve this problem, we need to use the formula for the force component in the direction of the tendon, which is given by F = Fm * cos(θ), where F is the force in the tendon, Fm is the force produced by the muscle fibers, and θ is the angle between the muscle fibers and the tendon.

In this case, we are given that F = 400 N and θ = 75°, and we need to find Fm. We can rearrange the formula to solve for Fm:

Fm = F / cos(θ)

Substituting the given values:

Fm = 400 N / cos(75°)

To get the answer, you need to calculate the value of cos(75°) and then divide 400 N by that value.

Please note that the angle should be in radians when using most calculators or programming languages. To convert from degrees to radians, you can use the formula radians = degrees * (π / 180). So, 75° is approximately 1.31 radians.

After calculating, you will get the force produced by the muscle fibers.