a particle of 8 kg is suspended by two light inextensible string that are inclined at the angles find the tension in the string when the particle in equilibrium​

T₁ = mg / (sinθ₁ + cosθ₁tanθ₂)

Τ₂ = T₁cosθ₁/cosθ₂

Explanation:

We are not given the angles, but if we assume that they are θ₁ and θ₂ as measured from the horizontal, and associated tensions are T₁ and T₂, we would need two equations to resolve them.

summing horizontal forces to zero

T₁cosθ₁ - Τ₂cosθ₂ = 0

summing vertical forces to zero

T₁sinθ₁ + Τ₂sinθ₂ - mg = 0

Τ₂ = T₁cosθ₁/cosθ₂

T₁sinθ₁ + (T₁cosθ₁/cosθ₂)sinθ₂ = mg

T₁(sinθ₁ + cosθ₁tanθ₂) = mg

T₁ = mg / (sinθ₁ + cosθ₁tanθ₂)

answer and explanation;

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