Can someone answer this question for me and please explain your reasoning for the answer. Amywho is 5ft tall casts a a4ft shadow when the pine tree has an 8ft shadow.How tall is the pine tree?
2007-01-25 18:46:17 · 13 answers · asked by llittle pee wee 1 in Science & Mathematics ➔ Botany
Both triangles are congruent. Because of this the proportions of the triangles will remain constant. The triangles are congruent because the sun is at a certain degree in the sky. It is the same in both cases. As long as the ground is flat... lol... the shadows will be caused by the sun being at this particular angle. We can make a right angle between the top of the tree and the ground and the tip of the shadow. We can do likewise with the human.
You can look at the following diagram to see what i'm talking about. The triangles might not look congruent but they are supposed to be.
http://i176.photobucket.com/albums/w173/lescientist/pinetreemath.jpg
Since they are congruent
5/4 = x / 8
If we cross multiply and divide we get x = 8*5/4 = 10
The pine tree is therefore 10 feet tall.
5/4 = x/8
2007-01-25 19:05:12 · answer #1 · answered by Le Scientist 2 · 1⤊ 0⤋
Pine Tree Casting
2017-01-15 10:54:57 · answer #2 · answered by ? 4 · 0⤊ 0⤋
24/10 = x/25 x = 24*25/10
2016-05-24 01:01:11 · answer #3 · answered by ? 4 · 0⤊ 0⤋
<>Assuming Amywho and the tree are casting shadows at the same time from the same place, make a proportion:
5' tall = 4' shadow
------- = -------------
x' tall = 8' shadow
Cross multiply:
4x = 40
divide:
x = 10 '....your tree is 10 ft tall.
2007-01-25 18:54:55 · answer #4 · answered by druid 7 · 1⤊ 0⤋
you have to set it up proportionally in an equation. both sides must be equal...
4/5=8/x the shadow height on top, actual height on bottom.
then solve algebraically for x
x=10 ft.
2007-01-25 18:57:04 · answer #5 · answered by Kelly 3 · 1⤊ 0⤋
The angle of the sun is an important factor in determining your answer.
2007-01-25 18:50:58 · answer #6 · answered by michelle 5 · 1⤊ 0⤋
actually it depends on what time if day it is, in the morning hours it could be a 1-3ft difference , in the after-noon it could be anywhere between a 6inch and one foot difference, this question is incomplete
2007-01-25 18:54:18 · answer #7 · answered by Anonymous · 0⤊ 0⤋
it depends on the angle of the sunshine to the tree causing the shadow, there is not enough information to answer your question!
2007-01-25 18:57:12 · answer #8 · answered by jsf19872005 2 · 1⤊ 1⤋
And - how high is the sun? What time of day? Which season? How long is a piece of string?
2007-01-25 18:53:05 · answer #9 · answered by Anonymous · 1⤊ 1⤋
6.4 feet is the answer based on 4' being 80% of 5', 80% of 8' is 6.4'.
2007-01-25 18:54:29 · answer #10 · answered by Anonymous · 0⤊ 1⤋