A person who is 6 feet tall walks away from flagpole toward the tip of the shadow of the flagpole. When the person is 30 feet from the flagpole, the tips of the person's shadow and the shadow cast by the flagpole coincide at a point 5 feet in front of the person. Find the height of the flagpole.

I probably going to need more to go on because if I knew how to do that (draw the model) I could have answered the problem already.

Your model is going to be two triangles. The larger triangle will be the flag pole, and inside that, you will have the person.

is it 42

To find the height of the flagpole, we can use similar triangles. Let's set up the problem and label the given information:

Let the height of the person be "x" feet.
Let the height of the flagpole be "h" feet.

Given:
- The person's height is 6 feet (x = 6).
- When the person is 30 feet from the flagpole, the tips of the person's shadow and the shadow cast by the flagpole coincide at a point 5 feet in front of the person.

To solve the problem, we need to establish a proportion using the similar triangles formed by the person, the flagpole, and their respective shadows.

In triangle ABD (person's triangle),
AB represents the person's height (x),
BD represents the length of the person's shadow.

In triangle CBD (flagpole's triangle),
CB represents the flagpole's height (h),
BD represents the length of the flagpole's shadow.

Since the tips of the person's shadow and the flagpole's shadow coincide at a point 5 feet in front of the person, we can say that BD = 30 - 5 = 25 feet.

Now, we can write the proportion based on the similar triangles:

AB/BD = CB/BD

Substituting the known values, we have:

6/25 = h/25

Simplifying the equation, we have:

6 = h

Therefore, the height of the flagpole is 6 feet.

Draw a diagram to model the situation. Then, set up a proportion.