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.