if a 6 foot person stands 10 foot from a 12 foot lamp post how long is his shadow? (how do you work that out)?

Answer 1

I won't give you the answer, just how to get it.

Draw the following two triangles as we go along.

The top of the lamp post, the base of the lamp post and the end of the shadow forms triangle 1.

The top of the head, the feet and the end of the shadow forms triangle 2.

Since the triangles are similar (same angles), the corresponding sides form a single ratio.

For example, the height of the triangles are 12 and 6 feet, respectively. They form a ratio of 12:6 (or 12/6).

The base of triangle 2 (the shadow) is x. The length of the shadow plus 10 feet is the base of triangle 1.

Therefore (10+x)/x = 12/6.

Now solve the problem.

Answer 2

I would first find the hypotenuse of the triangle taking into consideration that the shadow starts from the top of the persons head(I suppose that the lamp is to the right of him).
Therefore the adjacent is still 10 ft. but the opposite is 6 ft. -12ft (the length of the post) -6ft (the length of the person. Then use the Pythagorean to find the hypotenuse: 6^2+10^2= hypotenuse^2.
I am using the Pythagorean theorem because I assume the person is on level ground therefore virtually making it a right triangle. The hypotenuse equals square root of 136.
To get the angle at the top I would take the inverse sin of opposite/hypotenuse (Remember SOHCAHTOA). So since sin (angle)= O/H, sin^-1(6/(square root of 136))=angle.
Then I would find the opposite side of the triangle (the triangle to the left of the person)=shadow: we already that he is 6ft tall so that is the adjacent.
So, using the angle that we found earlier, Calculate the shadow: Since tan(angle)= opposite/adjacent, opposite=(tan(angle))*6=length of the shadow.

You must draw it out to get a better grasp on how the problem is answered.

Now looking at australeolive answer, him/her's is more simpler AND correct...should have drawn it out.:-P

Answer 3

It's triginometry. One side is the height of the lamp. then you have the distance between the lamp and the person, the distance between the person and the end of the shadow, and the distance between the top of the lamp and the top of the person.

What is the angle from the top of the lamp down to the top of the person? Work that out and you should find out how much further to the ground because the angle from the top of the person to the ground would be the same.

Answer 4

that's trigonometrie, a question of suinus and cosinus

you have 2 triangles with onesummit ( called A) that is the same (the one where the shadows stop) and you know that 6ft/size of the shadow = 12ft/10ft=tg(alpha) if alpha is the angle of the triangle at the point A

if X is the size of the shadow

X=(6*10)/12=60/12=5ft


make a draw and it's will become clearer

Answer 5

that's the same triangle problem. Say the guy stands x distance from the pole to achieve an 8 foot lengthy shadow. be conscious that the height of the guy and the 8 foot shadow sort a small triangle with the mild's projection. also be conscious that the 20ft pole and the dimensions from the pole to the shadow's tip yet another triangle with the mild's projection. be conscious that both triangles meet on the same aspect and characteristic the same attitude at that aspect (categorized it a). for this reason they're similar. because those triangles are similar, corresponding aspects have the same ratio. (imagine a line connecting b from a for the mild projection) b20ft | | 5.5 cost t | |_______|_______a -------x-----------8----- x is distance from pole 8 is length of shadow 5.5 is height of the guy 20 is height of pole x+8 is length to shadow tip (height pole/height of guy) = (length to shadow tip/ (length of shadow) So from the picture 20/5.5 = (x+8)/8 one hundred sixty = 5.5x + 40 4 116 = 5.5x x = 116/5.5 x = 21.0909 ft

Answer 6

a |
...|
...|
...|................c|
...|..................|
b |_________.d|_________e

In the above illustration let ab = length of lamp post = 12 ft
cd = height of person = 6 ft
bd = distance between lamp post and person = 10 ft
de = length of shadow = x ft

The triangles abe and cde are similar since they are right angle triangles.

Hence ab/cd = be/de (ratios of corresponding sides is the same)
so 12/6 = (10+x)/x (be = bd+de = 10+x)

2x = 10+x
so x = 10

So the length of his shadow will be 10 ft.

Hope this helps

Answer 7

p| m
|___|___s
o o'
let op be the pole of 12 ft, o'm person of 6 ft and o's length of shadow. oo'=10 ft

the two triangles ops and o'ms are similar as angles pos and mo's are equal and angles pso adn mso' are equal.

therefore
op / os = o'm / o's

=> 12 / (10 + o's) = 6 / o's
=> 12 o's = 60 + 6 o's
=> 6 o's = 60
=> o's = 10 ft
therefore the length of shadow = 10ft

Answer 8

it involves trigonometry here... i guess this is your homework. right? hehee.the answer is 10ft. use tangent formula........

you will have 2 right triangles here. one from the head to the top of the lamp post. from there you will get the angle... the other triangle will be from your head going to the end of your shadow, of course you will have same angle as the first triangle... thats how you will get the answer 10ft.... hope you get the picture... hehe....

Answer 9

10 ft?:) u need to draw the whole thing

Answer 10

What time is it?