Answer :
Answer:
Let x equal the length of the ladder.
Then the distance from the ground to the top of the ladder is (x-2).
The distance from the ladder to the building is 6.
The ground and the building wall form a right angle, therefore use Pythagorean Theorem.
x^2 = (x-2)^2 +6^2
x^2 = x^2 - 4x + 4 + 36
x^2 = x^2 - 4x + 40
Subtract x^2 from both sides leaving.
0 = -4x + 40
Add -40 to both sides.
-40 = -4x
Divide both sides by -4.
-40/-4 = -4x/-4
10 FEET = x THE LENGTH OF THE LADDER.
Answer:
24 feet
Step-by-step explanation:
The ladder leaning against the building resembles a right triangle. So, we can use the Pythagorean Theorem.
The Pythagorean Theorem is:
[tex]a^2+b^2=c^2[/tex]
Where a and b are the legs of the right triangle and c is the hypotenuse.
We know that the distance from the building is 7 feet. This means that the base is 7. So, we can substitute 7 into either a or b.
We know the ladder itself is 25 feet long. So, the hypotenuse is 25. Substitute that for c. Therefore:
[tex]7^2+b^2=25^2[/tex]
We need to solve for b to figure out how high up the building is the top of the ladder. Evaluate the squares:
[tex]49+b^2=625[/tex]
Subtract 49 from both sides:
[tex]b^2=576[/tex]
Take the square root of both sides:
[tex]b=24[/tex]
So, the top of the ladder is 24 feet up from the building.
And we're done!
