how tall is a telephone pole if it cast a shadow 24 feet long

To determine the height of a telephone pole based on the length of its shadow, you can use the concept of similar triangles. The ratios of corresponding sides of similar triangles are equal.

In this case, let's assume that the height of the telephone pole is represented by 'h' and the length of its shadow is 24 feet. We can also assume that the length of the shadow and the actual height of the pole form two sides of a right triangle, where the shadow is the base and the pole is the height.

Now, we can set up a proportion between the corresponding sides of two similar triangles:

height of the pole / length of the shadow = height of a similar triangle / length of the corresponding side

h / 24 = h / x

Here, 'x' represents the unknown length of the corresponding side (the height of a similar triangle).

To find 'x', we can cross-multiply the ratio and solve the equation:

h * x = 24 * h

x = (24 * h) / h

x = 24 feet

Therefore, if a telephone pole casts a shadow that is 24 feet long, the height of the pole will also be 24 feet.