Abox weighing 200 newtons is hanging from the ceiling. the value of angle 2 is 65°. tensions t1 and t2 are 132.6 newtons and 130.0 newtons respectively. what is angle 1?

According to Newtons third law vertical components of T₁ and T₂ should be equal to the weight of the box or:

T₁sin(θ₁) + T₂sin(θ₂)=200 N

Since θ₂=65°, T₁=132.6 N and T₂=130 N we need to solve for θ₁:

T₂sin(θ₂)=200 N - T₁sin(θ₁)

sin(θ₂)=(200-T₁sin(θ₁))/T₂

θ₂=sin⁻¹{(200-T₁sin(θ₁))/T₂}=37.9°

So the angle θ₂=37.9°.

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