Three trucks are pulling a weight. The middle truck is exerting a force of 1800 N at 96∘. The second and third trucks are positioned 21∘ on either side of the middle truck and are exerting forces of 3700 N and 3500 N, respectively. What is the magnitude of the resulting force? Round to the nearest whole number.

To find the resultant force, we can break down the forces into their horizontal and vertical components and then sum up the components separately.

For the middle truck:

Horizontal component = 1800 N * cos(96°)

Vertical component = 1800 N * sin(96°)

For the second truck:

Horizontal component = 3700 N * cos(21°)

Vertical component = 3700 N * sin(21°)

For the third truck:

Horizontal component = 3500 N * cos(-21°) (cosine of negative angle is the same as positive angle)

Vertical component = 3500 N * sin(-21°) (sine of negative angle is the negative of sine of positive angle)

Now, sum up the horizontal and vertical components separately:

Horizontal component sum = (1800 N * cos(96°)) + (3700 N * cos(21°)) + (3500 N * cos(-21°))

Vertical component sum = (1800 N * sin(96°)) + (3700 N * sin(21°)) + (3500 N * sin(-21°))

The magnitude of the resulting force can be calculated using the Pythagorean theorem:

Resulting force magnitude = √(Horizontal component sum)^2 + (Vertical component sum)^2

After performing the calculations, the magnitude of the resulting force is approximately 6927 N.

The magnitude of the resulting force exerted by the three trucks pulling the weight is approximately 6927 N.

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