So ( R = \frac200\sin\alpha = \frac200\sin 67.2° \approx \frac2000.922 \approx 216.9 , N).
Now slope of AI: (\tan(\alpha) = \fracy_I - 0x_I - 0 = \frac5 \sin50°2.5 \cos50° = 2 \tan50°). So ( R = \frac200\sin\alpha = \frac200\sin 67
So I = (2.5 cos50°, 5 sin50°).
Forces in x-direction: [ R_x = T \quad (\textsince R \text has a horizontal component toward the right) ] Forces in x-direction: [ R_x = T \quad
Ignore friction at the hinge.
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. Let's check: I is above and left of A
So ( R = \frac200\sin\alpha = \frac200\sin 67.2° \approx \frac2000.922 \approx 216.9 , N).
Now slope of AI: (\tan(\alpha) = \fracy_I - 0x_I - 0 = \frac5 \sin50°2.5 \cos50° = 2 \tan50°).
So I = (2.5 cos50°, 5 sin50°).
Forces in x-direction: [ R_x = T \quad (\textsince R \text has a horizontal component toward the right) ]
Ignore friction at the hinge.
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.