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!!!!?
a)


Let's consider the two triangles formed. The first one is made of your shadow and yourself, from head to toe. The second one if from your shadow to the light source (ground to where the lights is). These two triangles are similar because they are both right triangles (you and the light source are perpendicular to the ground), and the angle if the shadow to the top of you head to the light source is the common angle.





Let S represent the length of the shadow. So we have


S / (S + 12) = 6 / 18


18S = 6 (S + 12)


18S = 6S + 72


18S - 6S = 72


12S = 72


S = 72 / 12


S = 6 feet





b)


Let D represent your horizontal distance to the light source. Now let's re-do the above formula again, but this time, we'll solve for S in terms of D


S / (S + D) = 6 / 18


18S = 6 * (S + D)


18S = 6S + 6D


18S - 6S = 6D


12S = 6D


S = 6D/12


S = D/2





So as you can see, as your distance increases, so will the length of your shadow





c)


Now your distance is 24. So let's just plug that in the above formula and see what we get


S = D/2


S = 24/2


S = 12 feet





So your shadow is twice as long as before





I hope this helped





Kia