geometry help!!!?

Question

please i need some help: a tree 36 meters tall cracked in a violent earthquake and fell as if hinged. The tip of the once beautiful tree hit the ground 24 meters from the base. Researchers want to investigate the crack. How many meters up from the base of the tree do the researchers have to climb? ( i know that it has something to do with the pythagorean theorem and that the part of the tree that has fallen is 36-x).

Answer 1

You were so close!

so you have a triange that is 24m along the ground. The height you are looking for is x. and the hypotonuse is 36-x

a^2+b^2 = c^2
24^2 + x^2 = (36-x)^2
576 + x^2 = (36-x)(36-x)
576 + x^2 = 1296 - 72x - x^2
-720 = -72x
x = 10

Answer 2

Yup. We call the number of meters from the ground that the tree has cracked x, then the part of the tree that has fallen is 36-x. We have a right-angled triangle, and 36-x is the hypotenuse, and x and 24 are the cathetus. By Pythagoras' theorem, we have:

x^2 + 24 ^2 = (36-x)^2

x^2 + 576 = 36 ^2 -2 * 36 *x + x^2

x^2 + 576 = 1296 -72 *x + x^2 | -x^2

576 = 1296 -72 *x | +72x

576 + 72x = 1296 | -576

72x = 720 | :72

x = 10

Answer 3

okey dokey...
the tree cracked somewhere in the middle, so there's a piece coming out of the ground, then the broken part slants downward the ground, making a triangle.
the line from the tip of the tree, now touching the ground, to the base of the tree, is 24 meters. as you said, the cracked portion, the hypotenuse, is 36-x, and the portion that is still rooted and straight is represented as x. (this is because the entire tree is 36 m, so if one part is represented as x, the other is 36-x).
so now we use the pythagorean theorem.
hypotenuse squared = leg squared + leg squared...
242 + x^2 = (36-x)^2
576 + x^2 = 1296 - 72x + x^2
0 = 720 - 72x
-720 = -72x
x = 10
and there you have x, which is what we've said is the part still rooted, and that's what they'll have to climb... 10 meters.

Answer 4

You are right about using the pythagorean theorem
The hypothenuse of length x is the part of the tree that fall,
The hate of the part going from the base to the crack is therefore as you said 36-x
The length of the third part of the triangle is 24

Using the theoreme you have
x²=(36-x)²+24²
x²=1296 - 72 x + x² + 576
x=26 meters

Hence the remaining part standing is at 36 - x= 36 - 26 = 10 meters

Answer 5

Let x be the height of the still standing tree trunk
The part that has fallen over is 36 - x
Using the Pythagorean theorem:

x^2 + 24^2 = (36 - x)^2

Do the math:
x^2 + 576 = 1296 - 72 x + x^2

Combine like terms and rearrange:
x^2 - x^2 +72x = 1296 - 576
72x = 720

Solve:
x = 10

Answer 6

yes, you're right...draw a picture, and you'll see the part of the tree fallen (36-x) is the hypotenuse, 24 is one of the legs, and x (the height of the tree now) is the other leg
a^2 + b^2 = c^2
x^2 + 24^2 = (36-x)^2
x^2 + 576 = 1296 - 72x + x^2
x^2 = 720 - 72x +x^2
72x=720
x=10

Answer 7

a+b=36
a^-b^2=24^2

First equation is the fact that total height of tree is 36 m. Second equation is Pythagorean Theorem.

a = 36-b substitute this in the second equation:

(36-b)^2-b^2=576

Now you can solve and find b from one equation with one unknown, and then substitute that in the first equation to get a.

Answer 8

34 - 24 = 10

x=10 Simple! Hope this helps!

Answer 9

.....and the fallen part is the hypotenuse of a right triangle with legs x, 24 and hypotenuse of (36-x)-------
So, x² + 24² = (36-x)². Solve for x

I got 10.000....