SOLUTION: There is a bamboo tree 22 feet tall. The upper end of which, being broken, reaches the ground 8 feet from the stem. Find the height of the break?

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Question 1046156: There is a bamboo tree 22 feet tall. The upper end of which, being broken, reaches the ground 8 feet from the stem. Find the height of the break?
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
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Distance sum of hypotenuse and from base to the break is 22 feet. 8%2By=22
y=22-8
y=14

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
There is a bamboo tree 22 feet tall. The upper end of which, being broken, reaches the ground 8 feet from the stem. Find the height of the break?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let x be the height of the break.

Then you have an right angled triangle with the legs x ft and 8 ft.

The hypotenuse is sqrt%28x%5E2+%2B+8%5E2%29.

The height of the bamboo tree is  x+%2B+sqrt%28x%5E2+%2B+8%5E2%29, and it is equal to 22 ft.

Hence, the equation is 

x+%2B+sqrt%28x%5E2+%2B+8%5E2%29 = 22.

Simplify:

sqrt%28x%5E2+%2B+64%29 = 22 - x.

Square both sides

x%5E2+%2B+64 = %2822-x%29%5E2,  or

x%5E2+%2B+64 = 484+-+44x+%2B+x%5E2,

64 - 484 = -44x,

44x = 420,

x = 420%2F44 = 105%2F11 ft.

Answer.  The height of the break is 105%2F11 ft = 96%2F11 ft.

Check.  22+-+105%2F11 = 137%2F11.

        %28137%2F11%29%5E2+-+%28105%2F11%29%5E2 = 7744%2F121 = 64,

        sqrt%28%28137%2F11%29%5E2+-+%28105%2F11%29%5E2%29 = 8.   Correct!


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

There is a bamboo tree 22 feet tall. The upper end of which, being broken, reaches the ground 8 feet from the stem. Find the height of the break?
Let height of break be x ft

Then hypotenuse = 22 - x ft 

Length from stem (base) to point where upper end fell: 8 ft 

We then get: x%5E2+%2B+8%5E2+=+%2822+-+x%29%5E2

Solve for x: the height of break