How far was woodpecker above the ground?

Question

Woodpecker pecked at a 19m wooden pole until it cracked and the upper part fell with the top hitting the ground 10m from the foot of the pole. Since the upper part had not been broken completely woodpecker pecked away where the pole had cracked.

this is a Pythagorean theorem word problem and I don't understand how to set it up...

Answer 1

Assuming the pole was perpendicular to the ground when the woodpecker arrived, picture a right triangle.

Since the top was 10 m from the base, we know that one leg was 10 m, which means that the other leg plus the hypotenuse added to 19. We can express the leg as x and the hypotenuse as 19 - x

Applying the pythagorean theorem, we know that a2 + b2 = c2, or
102 + x2 = (19 - x)2

102 + x2 = 361 - 38x + x2

100 = 361 - 38x

38x = 261

x = 261/38 m or approx 6.87 m was the length of the pole remaining in the ground, and approx 12.13 m was toppled by the woodpecker.

Answer 2

the tree is going be perpendicular to the ground so there is the 90 degree angle.  The line on the ground from the base of the tree to the broken branch is 10m and because the branch broke you will subtract 10 from 19 to get 9 for the remainder of the tree.  so it will be set up as  9 squared plus 10 squared will equal c squared.

   

Answer 3

Great question.  

Picture in your in your mind what this looks like.  This is probably easiest to understand using graph paper.

Draw a vertical line 19 squares (representing 19m).

Then from the bottom of the pole draw a line 10m horizontally. Now "break" the vertical line so it connects to the horizontal line- but where?  

Enough of the pole had to break to fall 10m away from the bottom while still being attached at the top.  So break your pole so it hits 10m horizontally away from the bottom. If the two smallest line equals the length of the longest, you figured it out.