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.
