Two forces of 730 newtons and 670 newtons act simultaneously on an object. The angle between the two forces is 15°. Find the magnitude of the resultant, to the nearest newton.Find the measure of the angle between the resultant and the larger force, to the nearest 10th of a degree.

To solve this problem, we will use the law of cosines and the law of sines.

Step 1: Find the magnitude of the resultant force

The law of cosines states that c² = a² + b² - 2abcosC, where a and b are the sides of a triangle, C is the angle between them, and c is the side opposite angle C. In this case, the forces are the sides of the triangle (a and b), the angle between them is 15° (C), and the resultant force is the side opposite the angle (c).

So, we substitute the given values into the law of cosines:

c² = 730² + 670² - 2730670*cos(15°)

Calculate the values and solve for c (the resultant force).

Step 2: Find the angle between the resultant and the larger force

The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides of the triangle. In this case, we want to find the angle opposite the larger force (730 N), which we'll call A.

So, we set up the equation sinA/730 = sin(15°)/c, where c is the resultant force we found in step 1.

Solve for A to find the angle between the resultant and the larger force.

Remember to round your answers to the nearest newton and tenth of a degree, respectively.