the bottom of a 25-foot ladder is placed 7 feet from a wall. How far will the ladder reach up?
Since the ladder, wall, and ground form a right triangle, you can use this formula:
A squared + B squared = C squared
A = 7 feet
C = 25 feet
B = distance the ladder will reach
49 + B squared = 625
B squared = 625 - 49
B = square root of 576
B = 24 feet
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Therefore, the ladder will reach up 24 feet.
To find out how far the ladder will reach up, you can use the Pythagorean theorem. In this case, the ladder, the wall, and the ground form a right triangle.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
For this problem:
- The length of one side (A) is the distance from the bottom of the ladder to the wall, which is 7 feet.
- The length of the hypotenuse (C) is the length of the ladder, which is 25 feet.
- We need to find the length of the other side (B), which is how far the ladder will reach up.
Using the Pythagorean theorem, we can set up the equation:
A^2 + B^2 = C^2
Substituting the known values, we get:
7^2 + B^2 = 25^2
Simplifying this equation gives:
49 + B^2 = 625
To isolate B, we subtract 49 from both sides:
B^2 = 625 - 49
Simplifying further:
B^2 = 576
To solve for B, we take the square root of both sides:
B = √576
Calculating the square root of 576 gives:
B = 24 feet
So, the ladder will reach up to 24 feet.
To find out how far the ladder will reach up, you can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the hypotenuse.
In this case, the ladder serves as the hypotenuse, and the distance from the wall to the bottom of the ladder is one shorter side, while the distance the ladder will reach up is the other shorter side.
Using the formula A^2 + B^2 = C^2, where A is the length of one shorter side, B is the length of the other shorter side, and C is the length of the hypotenuse, we can plug in the known values.
Given:
A = 7 feet
C = 25 feet
Using the formula, we have:
7^2 + B^2 = 25^2
49 + B^2 = 625
Next, we subtract 49 from both sides of the equation:
B^2 = 625 - 49
B^2 = 576
To solve for B, we take the square root of both sides:
B = √576
B = 24 feet
Therefore, the ladder will reach up 24 feet.