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

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Question 1046158: There is a bamboo tree 22 feet tall. The upper part, 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(39620)   (Show Source): You can put this solution on YOUR website!
Same as #1045156.
14 feet.
Answer by ikleyn(52814)   (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 .

The height of the bamboo tree is  , and it is equal to 22 ft.

Hence, the equation is 

 = 22.

Simplify:

 = 22 - x.

Square both sides

 = ,  or

 = ,

64 - 484 = -44x,

44x = 420,

x =  =  ft.

Answer.  The height of the break is  ft =  ft.

Check.   = .

         =  = 64,

         = 8.   Correct!


Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

There is a bamboo tree 22 feet tall. The upper part, 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: 

Solve for x: the height of break 

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