Please help me smart people in math!!!!?

OKay.. this is the problem...


a. you are standing 12 feet from a light source 18 feet above the ground. if you are 6 feel tall, what is the lenght of the shadow that you will cast?


b. what will happen to the lenght of your shadow as you walk away from the light source? support your answers...





c. if you walk twice as far away from the light, will your shadow be twice as long?





please i really need help...

Please help me smart people in math!!!!?
I can`t draw a diagram on here, but I hope this will help:





Let the length of the shadow be x feet, so you have two similar right angled triangles, the legs being 18 and (12 + x) and in the other one, 6 and x. So:





6/x = 18/(12 + x) {both are the tangent of the angle of incination of the light at the end of the shadow} So:





6(12 + x) = 18x, so





72 + 6x = 18x, so





72 = 12x, so





x = 6.





Hope this helps, and I`ll let you try the next two parts, Twiggy.
Reply:To solve this problem, picture a right triangle as follows:





The light pole is the vertical leg. Its length is 18 feet.





The hypotenuse is the beam of light touching the top of your head and continuing to the tip of your shadow. We do not need to know its length.





The horizontal leg is the stretch of ground from the base of the light pole to the tip of your shadow. Its length is 12 feet plus the length of your shadow, which we'll call S.





Now, consider a similar triangle (one with the same angles as the first) with the vertical leg being a person (6 feet in length), and the horizontal leg being just the shadow (length S).





Because the angles on these two triangles are the same, the lengths of their sides will be proportionate: Thus the length of each side on the first triangle will be (18/6) = 3 times the length of the corresponding side on the second triangle.





So, 3 times the length of the shadow (the horizontal leg of triangle 2), or 3*S is equal to the length of 12+S (the horizontal leg on triangle 1).





With some simple algebra,


3*S = 12 + S =%26gt;


2*S = 12 =%26gt;


S = 6


we see that S, the length of the shadow, is 6 feet.








In response to part B, the shadow gets longer. Consider if you were 16 feet from the light pole. Then all of our information from before would remain the same, except for the length of the horizontal legs. Apply the same algebra with 16 feet instead of 12 feet, and you get:


3*S = 16 + S =%26gt;


2*S = 16 =%26gt;


S = 8,


so the shadow is now 8 feet long.


The further you move from the light pole, the more this will increase.





Finally, to address part C, if you are twice as far from the light pole, we use the same method, substituting 24 for 12 this time. Hence


3*S = 24 + S =%26gt;


2*S = 24 =%26gt;


S = 12.


Since the shadow is now 12 feet long, the answer is yes.





It's not as easy to explain it, in my opinion, without drawing a picture, but I hope this helps anyway.