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Given: sin(θ) = 2/√5, cos(θ) = 1/√5

The formula of tan(θ) is given as: tan(θ) = sin(θ)/ cos(θ)

This gives: tan(θ) = (2/√5)/ (1/√5) -> tan(θ) = (2/√5) * (√5/1) = 2/1.

Therefore, tan(θ) = 2/1

Cotangent of the angle θ is also written as cot(θ) is the reciprocal of tan(θ).

This implies: cot(θ) = 1/tan(θ)

Therefore, cot(θ) = 1/ (2/1) = 1/2.

Hence the value of cot(θ) = 1/2

Based on the question, here is the diagram.

The trigonometric function, sin(R) = (opposite side)/ (hypotenuse)

Therefore, sin(R) = PQ/PR

This gives: sin(30)= PQ/ 12 -> 1/2= PQ/ 12

This implies: PQ= 12 * 1/2 = 6

Therefore the measure of the side, PQ= 6m.