Torque formula is:

$\overline{){\mathbf{\tau}}{\mathbf{=}}{\mathbf{r}}{\mathbf{F}}{\mathbf{s}}{\mathbf{i}}{\mathbf{n}}{\mathbf{\theta}}}$

In this problem, we'll compute the angle between r and F from the equation:

$\overline{){\mathbf{\theta}}{\mathbf{=}}{\mathbf{c}}{\mathbf{o}}{{\mathbf{s}}}^{\mathbf{-}\mathbf{1}}{\mathbf{\left(}}\frac{\mathbf{r}\mathbf{.}\mathbf{F}}{\mathbf{\left|}\mathbf{r}\mathbf{\right|}\mathbf{\left|}\mathbf{F}\mathbf{\right|}}{\mathbf{\right)}}}$

We'll also use vector magnitude:

$\overline{){\mathbf{\left|}}{\mathbf{r}}{\mathbf{\right|}}{\mathbf{=}}\sqrt{{\mathbf{x}}^{\mathbf{2}}\mathbf{+}{\mathbf{y}}^{\mathbf{2}}\mathbf{+}{\mathbf{z}}^{\mathbf{2}}}}$

A wrench 40 cm long lies along the positive y-axis and grips a bolt at the origin. A force is applied in the direction (0, 4, -3) at the end of the wrench. Find the magnitude of the force needed to supply 90 N-m of torque to the bolt.

In order to find |F|, we will have to find the angle between F and r. We can use the equation

Using the equation above, we see that the angle is as follows. (Round your answer to one decimal place.)

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