If two people are taking a dog on a walk and have two leashes. One is at 18 degrees with a force of 23lbs and the other is at 15 degrees with 27lbs, how hard is the dog pulling if it holds them at a stand still?

To calculate the force with which the dog is pulling, we need to break down the forces acting on the dog in the horizontal and vertical directions.

First, let's convert the angles to their corresponding trigonometric functions.

The force acting on the dog at 18 degrees can be broken down into a horizontal component and a vertical component. The horizontal component is given by the force multiplied by the cosine of the angle: F1_horizontal = 23 lbs * cos(18°). Similarly, the vertical component is given by the force multiplied by the sine of the angle: F1_vertical = 23 lbs * sin(18°).

Applying the same logic to the force at 15 degrees, we get the following components: F2_horizontal = 27 lbs * cos(15°) and F2_vertical = 27 lbs * sin(15°).

To find the total horizontal and vertical forces acting on the dog, we sum up the individual components: F_horizontal_total = F1_horizontal + F2_horizontal and F_vertical_total = F1_vertical + F2_vertical.

Now, we can use the Pythagorean theorem to find the magnitude of the total force: F_total = sqrt(F_horizontal_total^2 + F_vertical_total^2).

Plugging in the values and calculating the force, we can find the answer.