a person 66 in tall is standing 15 ft from a streetlight. if the person casts a shadow 84 in long, how tall is the streetlight?
i know i have to set up a proportion. thanks for the help.
2006-09-15 01:28:35 · 8 answers · asked by shih rips 6 in Science & Mathematics ➔ Mathematics
Thes problem concerns two similar triangles
this problem can be solved through proportion
The first traingle equals
Height = 66 inches
The base equals 84 inches
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The second triangle
convert 15 ft to inches. 15 X 12 equals 180 Inches
84 + 160 = 264 inches
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Multiply the means by the extremes
66/h = 84/264
84h = 66(264)
84h = 17424
84h/84 = 17424/84
Dividing both sides of the equation by 84
h = 207.4285714 Inches
Convert 207.4285714 divided by 12 inches equals 17.28571429 ft
h = 17.28 ft rounded to two decimal places.
2006-09-15 05:12:36 · answer #1 · answered by SAMUEL D 7 · 0⤊ 0⤋
This is about similar triangles. Draw a line from the streetlamp to top of the person's head to the ground. The ground is the base for both triangles, and the person and the street lamps are the heights. Since they share a common angle, they are similar triangles, and the ratio of their bases and heights are equivalent.
15ft=180in
From the base of the streetlamp to the end of the shadow measures 180in+84in=264in
Let x = the height of the streetlamp
(66/84)=(264/x)
Multiply both sides by x:
x(66/84)=264
Multiply both sides by (84/66)
x(66/84)(84/66) = 264(84/66)
x = 264 (84/66)
Finish the arithmetic and divide by 12 to convert to feet.
2006-09-15 01:50:42 · answer #2 · answered by novangelis 7 · 0⤊ 0⤋
Similar triangles problem...just draw the triangles and get the relationships.
Distance from wall to end of shadow = 15 + 84/12 = 22 ft
side 1 (small triangle) = 66/12 = 5.5 ft
side 2 is your unknown
relationship:
side 2/distance from wall to shadow = side 1/shadow
side 2 = 5.5/7 * (22)
side 2 (streetlight post) = 17.28 ft
good luck.
2006-09-15 01:45:09 · answer #3 · answered by alrivera_1 4 · 0⤊ 0⤋
This is a very simple, straight forward question,
First convert the 15 feet in inches you get 180.
Utilizing the laws of proportion, and let the street light length = x :
x/66 = (84+180)/84
x = (84+180)*66/84
x= 207.42/12
x= 17.28 feet.
2006-09-15 03:10:48 · answer #4 · answered by lonelyspirit 5 · 0⤊ 0⤋
X/66 = (180+84)/84 = 207.42.....in or 17.28....Ft.
2006-09-15 02:15:15 · answer #5 · answered by Jack 2 · 0⤊ 0⤋
This is a similar triangles problem
|\
| .\
| .. \
| ...O -------------66in
| . -+-
| ....^ .\
| ../...\ .\
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15ft.. 84 in
The smaller triangle has height 66 inches and base 84 inches
The bigger triangle has base 84+180 inches - find the height
Ht/264 = 66/84
2006-09-15 01:38:05 · answer #6 · answered by Orinoco 7 · 0⤊ 0⤋
ought to the question be "2 vessels each and each contained equivalent parts of whiskey and water"....? If vessel A is composed of in hassle-free terms whiskey and vessel B is composed of in hassle-free terms water, he in hassle-free terms way the outline may be ultimate is that if before everything, each and each vessel contained precisely one teaspoon of the respective fluid.
2016-10-15 00:42:54 · answer #7 · answered by Anonymous · 0⤊ 0⤋
hope some data missing ...
2006-09-15 02:11:15 · answer #8 · answered by Manis 4 · 0⤊ 0⤋