We are given that Leah is 1.5 meters tall and when she walks 2.5 meters from the base of the pole towards the point where the cable is attached to the ground, her head just touches the cable.
To find the height of the pole, we need to determine the value of $X$.
We can set up a right triangle with the height of the pole as one side, the distance Leah walks as the other side, and the cable as the hypotenuse.
Using the Pythagorean theorem, we can write:
$(X + 1.5)^2 = 2.5^2 + X^2$
Expanding and simplifying the equation, we have:
$X^2 + 3X + 2.25 = 6.25 + X^2$
Subtracting $X^2$ from both sides of the equation, we get:
$3X + 2.25 = 6.25$
Subtracting 2.25 from both sides of the equation, we find:
$3X = 4$
Dividing both sides of the equation by 3, we get:
$X = \frac{4}{3}$
The value of X is $\frac{4}{3}$.
The answer is: 3
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
A telephone pole is supported by a steel cable which extends from the top of the pole to a point on the ground X meters from its base. When Leah walks 2.5 meters from the base of the pole toward the point where the cable is attached to the ground, her head just touches the cable. Leah is 1.5 meters tall. How many meters tall is the pole?
If we know the answer to the above question is 9, what is the value of unknown variable X?

### Answer:
