Juan and Anita are standing together in the schoolyard. Juan, who is 6 feet 2 inches tall, casts a shadow that is 54 inches long. At the same time, Anita casts a shadow that is 46 inches long. How tall is Anita?:

a. 86.4 in.
b. 5 ft 3 in.
c. 5 ft 1 in.
d. 64 in.

You have two similar triangles.

Set up ratios from each and solve.

5ft 1 in

To solve this problem, we can set up a proportion using the heights and shadows of Juan and Anita. We know that Juan, who is 6 feet 2 inches tall, casts a shadow that is 54 inches long. Similarly, Anita casts a shadow that is 46 inches long.

Let's define h as Juan's height in inches and x as Anita's height in inches.

The proportion can be set up as:

h / 72 = x / 46

To solve for x (Anita's height), we can cross-multiply and solve for x:

72x = 46h

Now, substitute Juan's height and shadow length into the equation:

72x = 46 * 74

Simplify the equation:

72x = 3348

Now divide both sides by 72:

x = 3348 / 72

x ≈ 46.5 inches

So, Anita's height is approximately 46.5 inches.

Now, we need to convert Anita's height from inches to feet and inches. Since there are 12 inches in a foot, divide 46.5 inches by 12 to get Anita's height in feet:

46.5 inches / 12 = 3.875 feet

Since it is more convenient to express height in feet and inches, we can convert 0.875 feet into inches by multiplying it by 12:

0.875 feet * 12 = 10.5 inches

Finally, add Anita's height in feet and inches:

3 feet + 10.5 inches = 4 feet 10.5 inches

Therefore, Anita's height is approximately 4 feet 10.5 inches.

None of the options provided match the result.