The heights of three Carpentry and Joinery students of a Technical Institute are 1.50m, xm and 1.45m. If the arithmetic mean height of the three students is 1.60m. calculate the value of x.

The arithmetic mean is the sum of all values divided by the number of values.
Given heights are $1.50 \, \text{m}$, $x \, \text{m}$, and $1.45 \, \text{m}$.
The number of students is 3.
The mean height is $1.60 \, \text{m}$.

$$\text{Mean} = \frac{\text{Sum of heights}}{\text{Number of students}}$$ $$1.60 = \frac{1.50 + x + 1.45}{3}$$

First, multiply both sides by 3:

$$1.60 \times 3 = 1.50 + x + 1.45$$ $$4.80 = 2.95 + x$$

Now, isolate $x$ by subtracting 2.95 from both sides:

$$x = 4.80 - 2.95$$ $$x = 1.85$$

The value of $x$ is $\boxed{\text{1.85 m}}$.