If a person bends at the waist with a straight back making an angle of Theta degrees with the horizontal, then the force F exerted on the back muscles can be modeled by the equation shown below, where W is the weight of the person. Complete parts (a) through (c) F=(0.6Wsin(Theta +90^circ ))/(sin12^circ ) (a) Calculate F when W=185lb and Theta =80^circ F=square lb (Round to the nearest pound as needed.)

To calculate the force \( F \) when \( W = 185 \) lb and \( \Theta = 80^\circ \), we will use the given formula:<br /><br />\[ F = \frac{0.6W \sin(\Theta + 90^\circ)}{\sin 12^\circ} \]<br /><br />First, let's break down the steps:<br /><br />1. Calculate \( \Theta + 90^\circ \):<br /> \[ \Theta + 90^\circ = 80^\circ + 90^\circ = 170^\circ \]<br /><br />2. Find the sine of \( 170^\circ \):<br /> Since \( 170^\circ \) is in the second quadrant, where sine is positive:<br /> \[ \sin 170^\circ = \sin (180^\circ - 10^\circ) = \sin 10^\circ \]<br /><br />3. Calculate \( \sin 10^\circ \):<br /> Using a calculator, we find:<br /> \[ \sin 10^\circ \approx 0.1746 \]<br /><br />4. Substitute the values into the formula:<br /> \[ F = \frac{0.6 \times 185 \times 0.1746}{\sin 12^\circ} \]<br /><br />5. Calculate \( \sin 12^\circ \):<br /> Using a calculator, we find:<br /> \[ \sin 12^\circ \approx 0.2079 \]<br /><br />6. Substitute \( \sin 12^\circ \) into the formula:<br /> \[ F = \frac{0.6 \times 185 \times 0.1746}{0.2079} \]<br /><br />7. Perform the multiplication and division:<br /> \[ F = \frac{0.6 \times 185 \times 0.1746}{0.2079} \]<br /> \[ F = \frac{32.178}{0.2079} \]<br /> \[ F \approx 154.5 \]<br /><br />Rounding to the nearest pound, we get:<br />\[ F \approx 155 \text{ lb} \]<br /><br />So, the force \( F \) is approximately \( 155 \) lb.