On a golf course, a flagstick casts a 150-inch shadow at the same time that a nearby tee casts a 5-inch shadow. If the tee is 234

Question

inches tall, how tall is the flagstick? Express your answer as a decimal if necessary.

Answer 1

To find the height of the flagstick, we can use the properties of similar triangles. The ratio of the height of the object to the length of its shadow will be the same for both the flagstick and the tee.

Let \( h \) be the height of the flagstick. Given that:

• The height of the tee is 234 inches, and the length of its shadow is 5 inches.
• The length of the flagstick's shadow is 150 inches.

We can set up the following proportion based on the concept of similar triangles:

\[ \frac{h}{150} = \frac{234}{5} \]

Now, we can solve for \( h \) by cross-multiplying:

\[ 5h = 234 \times 150 \]

Calculating the right side:

\[ 234 \times 150 = 35100 \]

So we have:

\[ 5h = 35100 \]

Now, divide both sides by 5 to find \( h \):

\[ h = \frac{35100}{5} = 7020 \]

Thus, the height of the flagstick is:

\[ \boxed{7020} \text{ inches} \]