a 17-foot ladder leans against a wall. if the ladder is 8 feet from the base of the wall, how far is it from the bottom of the wall to the top of the ladder
Let c = the length of the ladder. b = the distance from the wall. Use the Pythagorean theorem.
a^2 + b^2 = c^2
a^2 + 8^2 = 17^2
a^2 + 64 = 289
a^2 = 225
a = 15
15ft
imagine a triangle. The diagonal side is 17 ft. the bottom is 8 ft. Use the pythagorean theorem to find the third side. so
17^2 minus 8^2 = 225. then take the square root of 225, which is 15
my way worked too
Yep. It's always good to show students more than one way to solve a problem.
Btw -- I hadn't seen your post when a posted mine.
*I posted mine.
oh ok :)
A ladder with length 20m. stands vertically against a wall. How much further should the lower end of the end of the ladder be moved so that its upper end descends 4 metre?
My 20 foot ladder was about 8 feet from the wall and by the time my face busted on the rock below I didn't do any measuring.
I drove to the hospital and got many stitches.
15
To find the distance from the bottom of the wall to the top of the ladder, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this scenario, the ladder acts as the hypotenuse, the distance from the bottom of the wall to the base of the ladder acts as one side, and the distance from the base of the ladder to the top of the wall acts as the other side.
Let's assign variables to the different values:
- Length of the ladder (hypotenuse): c = 17 feet
- Distance from the bottom of the wall to the base of the ladder (one side, adjacent to the angle): a = 8 feet
- Distance from the base of the ladder to the top of the wall (other side, opposite to the angle): b = ?
Now, we can use the Pythagorean theorem to solve for b:
c^2 = a^2 + b^2
Substituting the given values:
(17 ft)^2 = (8 ft)^2 + b^2
Simplifying:
289 ft^2 = 64 ft^2 + b^2
Rearranging the equation to solve for b:
b^2 = 289 ft^2 - 64 ft^2
b^2 = 225 ft^2
Taking the square root of both sides:
b = sqrt(225 ft^2)
b = 15 ft
Therefore, the distance from the bottom of the wall to the top of the ladder is 15 feet.