Forces with magnitudes of 2000 newtons and 900 newtons act on a machine part at angles of 10° and 85° respectively, with the x-axis. find the direction and the magnitude of the resultant of these forces. round to the nearest tenth place.

First, you need to find the components of each force:

F₁x = 2000 cos10 = 1969.6 N

F₁y = 2000 sin10 = 347.3 N

F₂x = 900 cos85 = 78.4 N

F₂y = 900 sin85 = 896.6 N

Then, you have to sum up the same components of the two forces:

Rx = F₁x + F₂x = 1969.6 + 78.4 = 2048.0 N

Ry = F₁y + F₂y = 347.3 + 896.6 = 1243.9 N

In order to find the magnitude of the resultant, you need to apply the Pythagorean theorem:

R = √ (Rx² + Ry²)

= √ 2048.0² + 1243.9²

= 2396.2 N

Now, in order to find the direction (angle), you need to use a bit of trigonometry:

α = tan⁻¹ (Ry / Rx)

= tan⁻¹ (1243.9 / 2048)

= tan ⁻¹ (0.60737)

=31.3°

Therefore, the answer is: the resultant has a magnitude of 2396.2N with an angle of 31.3° with respect to the x-axys.