Solving a triangle????? URGENT HELP <span title="NEEDED!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!?">NEEDED!!!!!!!!!!!!!!!!!!!...</span>

Question

A light, on top of a post, is 14 feet above the ground. At night a 5 foot woman is standing 18 feet from the post. The woman's shadow is 10 feet long. Her friend is standing 16 feet away from the post.

Starting 18 feet from the post, the woman walks directly away from the post for 4 seconds at a rate of 3 feet per second. Find the average speed(average speed = total distance/total time) on the tip of her shadow during that 4 second interval

http://i37.tinypic.com/2us8y7s.jpg

How do i solve this...

Answer 1

okay so at time = 0s she hasn&#039;t moved and her shadow is 10ft long.

at time = 4s she has moved 12 ft. she is now 30ft away from the lampost. use similar triangles to figure out her new shadow length:

o

|

|----------------o

|____30&#039;___|___x&#039;__

the big triangle has 14&#039; leg and (30+x) base

the smaller one has 5&#039; leg and x&#039; base

set up a proportion:

14/5 = (30+x)/x

cross multiply:

14x = 5(30+x)

14x = 150 +5x

9x = 150

x = 150/9 = 50/3

so in 4 seconds the shadow went from 10ft to 50/3ft.

average shadow speed = (50/3 -10)ft/4s

ave = (20/3)ft/4s

ave = 5/3 ft per second

Answer 2

hope you have had calculus...let the entire length be S and let x = distance from the woman to the pole. Then you have similar triangles with 14 / S = 5 /( S - x) or  9 S = 14 x ---&gt; derivative yields dS / dt = [14 / 9 ] dx / dt, but dx / dt is given as 3 {ft/sec}. Hence dS / dt =  14 / 3 {ft/sec}...this is how fast the tip is moving....note: the shadow is lengthening at a rate of  5/3 {ft/sec}

Answer 3

let shadow&#039;s tip total distance be d.

x / 5 = (18 + 3*4 + x) / 14

x / 5 = (x + 30) / 14

14x = 5x + 150

9x = 150

x = 150 / 9 = 50 / 3

d = (x + 30) - (10 + 18)

= 50/3 + 2

= 56/3

average speed

= d / (4 seconds)

= 56 / 3*4

= 14 / 3

= 4.667 feet per second