You are fi ve feet tall and cast a seven-foot
eight-inch shadow. At the same time, a basketball
hoop casts a 19-foot shadow. How tall is the
basketball hoop? Assume the triangles
are similar.
Change it into to inches. So 5= 60
7 and 8" is= 92 and 19= 228.
60/92 = x/228. SOlve the proportion to get x is about = to 149. Divide by 12 and you get about 12 feet tall.
To find the height of the basketball hoop, we can set up a proportion using the similar triangles formed by the height of you and the height of the basketball hoop, as well as the length of your shadow and the length of the basketball hoop's shadow.
Let's denote the height of the basketball hoop as "x".
The proportion can be set up as follows:
(height of you) / (length of your shadow) = (height of the basketball hoop) / (length of the basketball hoop's shadow)
Substituting the given values:
5 feet / 7 feet 8 inches = x / 19 feet
First, let's convert the length of your shadow to feet. Since there are 12 inches in a foot, 8 inches is equal to 8/12 = 2/3 feet. Therefore, the length of your shadow is 7 feet and 2/3 feet.
Simplifying the proportion:
5 feet / 7 2/3 feet = x /19 feet
To get rid of the mixed fraction, we can convert 7 2/3 feet to an improper fraction. Multiplying the whole number (7) by the denominator (3), we get 7 * 3 = 21. Adding the numerator (2), we have 21 + 2 = 23. Thus, 7 2/3 feet can be written as 23/3 feet.
Substituting this value into the proportion:
5 feet / 23/3 feet = x / 19 feet
To divide by a fraction, we multiply by its reciprocal:
5 feet / (23/3 feet) = (5 feet) * (3 feet/23 feet) = 15/23 feet
Now, our proportion becomes:
15/23 feet = x / 19 feet
To solve for x, we cross multiply:
(15/23 feet) * (19 feet) = x
Calculating:
(15 * 19) / 23 = x
285 / 23 = x
x ≈ 12.39 feet
Therefore, the basketball hoop is approximately 12.39 feet tall.
To find the height of the basketball hoop, we can use the concept of similar triangles.
Similar triangles are triangles that have the same shape but differ in size. In this case, we can compare the height and shadow of the person to the height and shadow of the basketball hoop.
Let's set up a proportion using the corresponding sides of the two triangles:
(person's height) / (person's shadow) = (basketball hoop's height) / (basketball hoop's shadow)
Substituting the given values:
5 feet / 7 feet 8 inches = (basketball hoop's height) / 19 feet
To simplify the equation, we need to convert 7 feet 8 inches into a single unit of measurement. Since 1 foot is equal to 12 inches, we can convert 7 feet into 84 inches. Therefore, the person's shadow is 84 + 8 = 92 inches.
Substituting the converted values:
5 feet / 92 inches = (basketball hoop's height) / 19 feet
Now, let's solve for the basketball hoop's height:
Cross-multiplying:
(5 feet) * (19 feet) = (basketball hoop's height) * (92 inches)
95 feet = (basketball hoop's height) * 92 inches
To isolate the basketball hoop's height, we divide both sides of the equation by 92:
(95 feet) / 92 = (basketball hoop's height)
Calculating this value:
95 / 92 ≈ 1.03 feet
Therefore, the height of the basketball hoop is approximately 1.03 feet or about 12.4 inches.