Verify that the equation is an identity.
-When a person bends at the waist with a straight back, the force, F, exerted by the person's lower back muscles can be estimated with the formula $F = 2.89 \mathrm { w } \sin \left( \theta + 90 ^ { \circ } \right)$, where $w$ is the person's weight, and $\theta$ is the angle made by the person's torso relative to the horizontal. Suppose that a 220 -pound person bends at an angle of $30 ^ { \circ }$. Determine the force exerted by the person's back muscles, and estimate the angle that requires the back muscles to exert a force of 381 pounds. Round the force to the nearest pound, and the angle to the nearest tenth, if necessary.
A) 318 pounds; $47.3 ^ { \circ }$
B) 551 pounds; $30 ^ { \circ }$
C) 551 pounds; $53.2 ^ { \circ }$
D) 26 pounds; $53.2 ^ { \circ }$

Question

Quizplus · Accepted Answer

The force exerted is calculated as $F = 2.89 \times 220 \times \sin(120^\circ)$, which equals approximately 551 pounds. Solving for the angle when the force is 381 pounds gives $\theta \approx 53.2^\circ$.

Verify That the Equation Is an Identity F=2.89wsin⁡(θ+90∘)F = 2.89 \mathrm { w } \sin \left( \theta + 90 ^ { \circ } \right)F=2.89wsin(θ+90∘)

Verify That the Equation Is an Identity $F = 2.89 \mathrm { w } \sin \left( \theta + 90 ^ { \circ } \right)$