If the boy is 4' 9" tall and his shadow is 6 ft. and the shadow of the flagpole is 19 ft., determine the height of the flagpole (to the nearest tenth).

Question

If the boy is 4' 9" tall and his shadow is 6 ft. and the shadow of the flagpole is 19 ft., determine the height of the flagpole (to the nearest tenth).

Answer 1

using ratios

4'" = 4.75'

4.75 : 6 = x : 19
4.75/6 = x/19
cross multiply
90.25 = 6x
x = 15.04167
x = 15
check my math, it's late for me

Answer 2

To determine the height of the flagpole, we can set up a proportion using similar triangles.

Let's define:
- Height of the boy as B
- Shadow of the boy as SB
- Shadow of the flagpole as SF
- Height of the flagpole as F

The proportion we can set up is:
(B / SB) = (F / SF)

We are given:
SB = 6 ft
SF = 19 ft
B = 4' 9" (since the boy is 4' 9" tall, we need to convert this to feet)

To convert 4' 9" to feet, we divide by 12 (since there are 12 inches in a foot):
B = 4 + (9 / 12) = 4.75 ft

Now we can substitute the known values into the proportion and solve for F:

(4.75 / 6) = (F / 19)

To isolate F, we can cross-multiply:

4.75 * 19 = 6 * F

90.25 = 6 * F

Now, divide both sides by 6:

90.25 / 6 = F

F ≈ 15.04 ft

Therefore, the height of the flagpole is approximately 15.04 feet.

Answer 3

To determine the height of the flagpole, we can use a proportion based on the similar triangles formed by the boy, his shadow, and the flagpole's shadow.

Let's let "x" represent the height of the flagpole.

First, we convert the height of the boy and his shadow to the same unit as the flagpole's shadow. Since the shadow of the flagpole is given in feet, we need to convert the boy's height from feet and inches to feet:
The boy's height is 4' 9". We can convert this to feet by multiplying the number of feet (4) by 12 (since there are 12 inches in a foot) and adding the extra inches (9 inches), which gives us a total of 57 inches.
To convert this to feet, divide 57 inches by 12, which gives us the value of 4.75 feet.

Now we can set up a proportion using the boy's height, the boy's shadow, the flagpole's shadow, and the height of the flagpole as follows:
(Height of the boy)/(Length of the boy's shadow) = (Height of the flagpole)/(Length of the flagpole's shadow)

Plugging in the values we have:
4.75/6 = x/19

To solve for x, we can cross-multiply and then divide:
4.75 * 19 = 6x
90.25 = 6x
x = 90.25/6
x ≈ 15.04

Therefore, the height of the flagpole is approximately 15.04 feet, rounded to the nearest tenth.