Aforce of 5n and a force of 8n act to the same point and are inclined at 45degree to each other. find the magnitude and direction of the resultant force.

Refer to the diagram attached (created with GeoGebra). Consider the 5 N force in two directions: parallel to the 8 N force and normal to the 8 N force.

The sum of forces on each direction will be the resultant force on that direction:

Apply the Pythagorean Theorem to find the magnitude of the resultant force.

(3 sig. fig.).

The size of the angle between the resultant force and the 8 N force can be found from the tangent value of the angle. Tangent of the angle:

.

Find the size of the angle using inverse tangent:

.

In other words, the resultant force is 17.0° relative to the 8 N force.

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