The attachment point of the cable holding the flask in a vertical position is at a subtraction of 12 m from the ground.

The attachment point of the cable holding the flask in a vertical position is at a subtraction of 12 m from the ground. The distance from the base of the flask to the place where the cable is attached to the ground is 9 m. Find the length of the cable.

If we depict the condition of the problem in the figure, we will get a right-angled triangle in which two legs are known: the height of the flagpole and the distance from the base of the flagpole to the place of attachment of the cable.
By the Pythagorean theorem, we find the hypotenuse – the length of the cable.
√ (12² + 9²) = √ (144 + 81) = √ 225 = 15 (m).
Answer: the length of the cable is 15 m.