Question

You are doing exercises on a nautilus machine in a gym to strengthen your deltoid (shoulder) muscles. Your arms are raised vertically and can pivot around the shoulder joint, and you grasp the cable of the machine in your hand 64.0 cm from your shoulder joint. The deltoid muscle is attached to the humerus 15.0 cm from the shoulder joint and makes a 12.0° angle with that bone. What is the distance between the attachment point of the deltoid muscle and the cable of the machine?

1) 79.0 cm
2) 49.0 cm
3) 29.0 cm
4) Cannot be determined

Answer 1

The distance between the attachment point of the deltoid muscle and the cable on the nautilus machine cannot be determined with the given information, as key measurements are missing to apply trigonometric principles.

Step-by-step explanation:

To calculate the distance between the attachment point of the deltoid muscle and the cable on the nautilus machine, we can use the law of cosines if we consider the shoulder joint, the attachment point of the deltoid on the humerus, and the hand holding the cable as vertices of a triangle. However, to utilize the law of cosines, we would need three sides or two sides, and the included angle which we do not have here. We only know the length of the arm (the distance from the cable to the shoulder joint) and the position of the deltoid attachment. Without further information, such as the horizontal distance from the shoulder joint to the point where the deltoid muscle is attached, we cannot determine the distance between the cable and the attachment point of the deltoid muscle using trigonometry. Given the current information, the answer is (4) Cannot be determined.