SOLUTION: I need help! how do i fing the answer to this problem? a bamboo stick thats 20 ft long breaks and the tip touches 5 ft from the base. what is the height? how do i do this!!

Question 262151: I need help! how do i fing the answer to this problem? a bamboo stick thats 20 ft long breaks and the tip touches 5 ft from the base. what is the height? how do i do this!!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
bamboo stick that's 20 ft long breaks. and the tip touches 5 ft from the base. what is the height? how do i do this!!
:
A right triangle problem; a^2 + b^2 = c^2; draw a picture of this situation
:
Let a = 5, the distance from the base to the tip, which now touches the ground
We know
b + c = 20 feet (vertical height + the part that touches the ground 5'away)
which is:
b = (20-c)
:
Remember a^2 + b^2 = c^2. Replace a and b, and find c
:
5^2 + (20-c)^2 = c^2
25 + 400 - 40c + c^2 = c^2; (FOIL (20-c)(20-c)
425 - 40c + c^2 - c^2 = 0; (c^2's cancel)
425 = 40c
c =
c = 10.625 ft, the part that slants to the ground
then
20 - 10.625 = 9.375 ft, the height of the bent bamboo
;
:
Check this on a calc:
5^2 + 9.375^2 = 10.625^2
25 + 87.89 = 112.89
112.89 = 112.89; confirms our solution

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