Ignore friction at the hinge.
Question: Trouvez les tensions ( T_1 ) et ( T_2 ) dans les câbles.
Then equilibrium: Horizontal: ( R\cos\alpha = T ), Vertical: ( R\sin\alpha = W = 200 ) N. Ignore friction at the hinge
Also, moment equilibrium (or concurrency) gives: The line of ( R ) must pass through I.
Forces in y-direction: [ R_y = W = 200 , N ] Also, moment equilibrium (or concurrency) gives: The line
Forces in x-direction: [ R_x = T \quad (\textsince R \text has a horizontal component toward the right) ]
So I = (2.5 cos50°, 5 sin50°).
Numerically: (\tan50° \approx 1.1918) → ( \tan\alpha \approx 2.3836) → ( \alpha \approx 67.2°) above horizontal? That seems too steep. Let's check: I is above and left of A? No, A is at origin, I has x positive (2.5cos50°=1.607), y positive (5sin50°=3.83). So R points up-right? But rope pulls left, so hinge must pull right-up to balance. Yes, so R angle ≈ 67° from horizontal upward right.