SOLUTION: Help me solve this problem please A six foot man is standing atop a 9 foot wall. The distance along the hypotenuse from the top of the man's head to the ground is 17 feet. Kneel

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Question 855629: Help me solve this problem please
A six foot man is standing atop a 9 foot wall. The distance along the hypotenuse from the top of the man's head to the ground is 17 feet. Kneeling children are lined up at the base of the wall. Each kneeling child takes up 1 foot of horizontal space. How many children can kneel along the bottom of the triangle? Assume the wall and the man are vertical, forming a right trial with the ground.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
This looks like the first part of a 3-part problem asked as question 855638, question 855639, and question 855640.
Here is a copy of my previous answer.

a) A 6 foot man is standing atop a 9 foot wall The distance along the hypotenuse from the top of the man's head to the ground is 17 feet. Kneeling children are lined up at the base of the wall. Each kneeling child takes up 1 foot of horizontal space.
There is a green right triangle with leg measures x and 15 feet, and hypotenuse measuring 17 feet.
According to the Pythagorean theorem
x%5E2%2B15%5E2=17%5E2-->x%5E2%2B225=289-->x%5E2=289-225-->x%5E2=64--> x=sqrt%2864%29--> highlight%28x=8%29
The horizontal space along the bottom of the triangle is highlight%28x=8%29 ,
so highlight%288%29 kneeling children (each one taking up 1 foot of horizontal space fit on that leg of the right triangle.

b)The man jumps off the original wall and 4 children are removed from the left side of the line. A new triangle is formed. What is the length of the hypotenuse of the new triangle measured from the top of the wall to the ground?
With 8-4=4 children left, the horizontal leg of the new right triangle measures only 4feet .
The vertical lefg measures 9+feet , the height of the wall.
The Pythagorean realation for the length in feet is:
y%5E2=4%5E2%2B9%5E2-->y%5E2=16%2B81-->y%5E2=97-->y=sqrt%2897%29=9.85 (rounded).
The length of the hypotenuse of the new triangle is approximately
highlight%289.85feet=9feet10inches%29 .

c) Each child on the ground (from the original triangle in part a) lies down head to toe, taking up 3 feet each. The 6 foot man is still standing on top of the wall, but the wall is shorter now. If the distance along the hypotenuse from the top of the man's head to the ground is exactly 26 feet, what is the new exact height of the wall?
The horizontal leg measures 8%2A3=24ft and the hypotenuse measures 26ft.
If ft.
According to the Pythagorean theorem
%286%2Bw%29%5E2%2B24%5E2=26%5E2-->%286%2Bw%29%5E2%2B576=676-->%286%2Bw%29%5E2=674-576-->%286%2Bw%29%5E2=100--> 6%2Bw=sqrt%28100%29-->6%2Bw=10-->w=10-6-->highlight%28w=4%29
The new height of the wall is highlight%284feet%29 .