A 24 foot tall tree was hit by a lightning storm, cracked, and fell over. After it broke, the top of the tree touched the gorund 12 feet from the base of the tree. How tall is the part of the tree still left standing?
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Hello
The tree was 24 feet tall.
Say it was broken at heigth x
The broken part is 24 - x
This broken part it the hypotenuse of a right triangle with other sides 12 and x
then
x² + 12² = (24 - x)²
x² + 144 = 576 - 48x + x²
x² - x² + 144 - 576 + 48x = 0
48x - 432 = 0
48x = 432
x = 432 / 48 = 9
The part of the tree still standing is 9 feet
Hope it helped
It is fair to select a best answer, whatever it is. Thank you !
Bye !
The tree was 24 feet tall.
Say it was broken at heigth x
The broken part is 24 - x
This broken part it the hypotenuse of a right triangle with other sides 12 and x
then
x² + 12² = (24 - x)²
x² + 144 = 576 - 48x + x²
x² - x² + 144 - 576 + 48x = 0
48x - 432 = 0
48x = 432
x = 432 / 48 = 9
The part of the tree still standing is 9 feet
Hope it helped
It is fair to select a best answer, whatever it is. Thank you !
Bye !
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Let call the part of the tree that left standing is x
The tree is 24 feet so the part that fell over is (24 - x) and it is also the hypotenuse.
Now you have a right triangle with
1 leg is x
the other leg is 12 feet
and the hypotenuse is (24 - x)
Using Pythagorean Theorem
(24 - x)² = x² + 12²
576 - 48x + x² = x² + 144
-48x = -432
x = 9
The part the left standing is 9 feet
The tree is 24 feet so the part that fell over is (24 - x) and it is also the hypotenuse.
Now you have a right triangle with
1 leg is x
the other leg is 12 feet
and the hypotenuse is (24 - x)
Using Pythagorean Theorem
(24 - x)² = x² + 12²
576 - 48x + x² = x² + 144
-48x = -432
x = 9
The part the left standing is 9 feet
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9 Feet Tall.
Draw a triangle where the vertical side, one of the legs, is the part of the tree left standing, and call it x. Make the base, or the second leg, 12 feet. Make the hypotenuse, the part of the tree that fell, equal to 24-x feet, because we know that the part left standing PLUS the part that fell equals 24 feet.
Using the Pythagorean theorem, which is a^2 + b^2 = c^2, we use the formula (12)^2 + x^2 = (24-x)^2.
This means that 144 + x^2 = 576 - 48x + x^2.
Subtract x^2 from both sides, you end up with 144 = 576 - 48x.
Add 48x to both sides, you end up with 48x + 144 = 576.
And finally, subtracting 144 from both sides, you end up with 48x = 432
Divide both sides by 48, and x = 9 feet.
We labeled the standing part of the tree as x, so you have just found the answer, which is 9 feet tall.
Draw a triangle where the vertical side, one of the legs, is the part of the tree left standing, and call it x. Make the base, or the second leg, 12 feet. Make the hypotenuse, the part of the tree that fell, equal to 24-x feet, because we know that the part left standing PLUS the part that fell equals 24 feet.
Using the Pythagorean theorem, which is a^2 + b^2 = c^2, we use the formula (12)^2 + x^2 = (24-x)^2.
This means that 144 + x^2 = 576 - 48x + x^2.
Subtract x^2 from both sides, you end up with 144 = 576 - 48x.
Add 48x to both sides, you end up with 48x + 144 = 576.
And finally, subtracting 144 from both sides, you end up with 48x = 432
Divide both sides by 48, and x = 9 feet.
We labeled the standing part of the tree as x, so you have just found the answer, which is 9 feet tall.
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A squared x 12 squared = 24 squared
A squared x 144 = 573
*subtract 144 from both sides*
A squared = 432
A = square root of 432 or 20.8
Sorry if this is a little confusing, it's weird typing out math equations like this. Good luck :)
A squared x 144 = 573
*subtract 144 from both sides*
A squared = 432
A = square root of 432 or 20.8
Sorry if this is a little confusing, it's weird typing out math equations like this. Good luck :)
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A squared plus B squared equals C squared. Draw the triangle so you can see the image square the two known numbers and add the together. Find the square root of that number and you will have your answer.
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This EXACT SAME question was in my geometry book! The answer is 6 because 12 is the hypotenuse. So 6 squared plus 6 squared = 12 squared. So the answer would have to be six