Question

In the lake, a sailboat casts a shadow of 4 yards. A buoy that is 2 feet tall casts a shadow of 1 foot.

What is the height of the sailboat?



2 feet
6 feet
24 feet
8 feet

Answer 1

To find the height of the sailboat, we can use the concept of similar triangles. The ratios of the height of an object to the length of its shadow will be the same for both the buoy and the sailboat.

Let:
- \( h \) = height of the sailboat (in feet)
- The height of the buoy is 2 feet, and it casts a shadow of 1 foot.
- The shadow of the sailboat is 4 yards. Since we need to work in the same units, we'll convert this measurement to feet. There are 3 feet in a yard, so:

\[
4 \text{ yards} = 4 \times 3 = 12 \text{ feet}
\]

Now we can set up a proportion based on the similar triangles formed by the objects and their shadows:

\[
\frac{h}{12} = \frac{2}{1}
\]

Now we solve for \( h \):

\[
h = 12 \times \frac{2}{1} = 12 \times 2 = 24 \text{ feet}
\]

Thus, the height of the sailboat is \( \boxed{24} \) feet.