a man who is 5 feet tall stands 15 feet from a lamppost that is 27 feet high. how far away from the man is the tip of his shadow?

sorry i forgot to say that i don't need the answer... i need an equation or expression that models this situation.

s/(15+s) = 5/27

or

(15+s)/27 = s/5

To find the distance from the man to the tip of his shadow, we can use similar triangles. Let's label the height of the man as 'h', the distance from the man to the lamppost as 'd', and the height of the lamppost as 'H'.

We know that the height of the lamppost is 27 feet, so H = 27 feet. The man's height is 5 feet, so h = 5 feet.

Now, let's set up a proportion using the similar triangles formed by the man, the shadow, and the lamppost:

h / H = d / (d + x)

where 'x' represents the distance from the man to the tip of his shadow.

Substituting the known values, we have:

5 / 27 = 15 / (15 + x)

To solve for 'x', we can cross-multiply:

5(15 + x) = 27 * 15

75 + 5x = 405

Subtracting 75 from both sides:

5x = 405 - 75

5x = 330

Dividing both sides by 5:

x = 330 / 5

x = 66

Therefore, the tip of the man's shadow is 66 feet away from him.