The bottom of a ladder must be placed 5 ft. from a wall. The ladder is 12 feet long.
what is the distance in feet from the ground that the ladder reaches the wall? Round to the nearest tenth.
Using the Pythagorean theorem, we can solve for the height that the ladder reaches on the wall.
The ladder, the distance from the wall, and the height on the wall form a right triangle.
Using the formula: a^2 + b^2 = c^2, where c is the length of the ladder (12 ft).
Let a be the height on the wall and b be the distance from the wall.
We know that b is 5 ft and c is 12 ft.
a^2 + 5^2 = 12^2
a^2 + 25 = 144
a^2 = 144 - 25
a^2 = 119
a ≈ √119
a ≈ 10.91 ft
Therefore, the distance from the ground that the ladder reaches on the wall is approximately 10.91 feet.
To find the distance from the ground that the ladder reaches the wall, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the ladder acts as the hypotenuse, the distance from the wall to the bottom of the ladder is one side, and the distance from the ground to the bottom of the ladder is the other side.
Let's name the distance from the wall to the ladder's bottom x, and the distance from the ground to the ladder's bottom y.
We can set up the equation as follows:
x^2 + y^2 = 12^2
Since we know that the bottom of the ladder must be placed 5 ft. from the wall (x = 5), we can substitute it into the equation:
5^2 + y^2 = 12^2
25 + y^2 = 144
Now, subtract 25 from both sides to isolate y^2:
y^2 = 144 - 25
y^2 = 119
We can take the square root of both sides to solve for y:
y = √119
Now, let's round the value √119 to the nearest tenth:
y ≈ 10.9
Therefore, the distance in feet from the ground that the ladder reaches the wall is approximately 10.9 feet.
To find the distance in feet from the ground that the ladder reaches the wall, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In this case, the ladder acts as the hypotenuse of the right-angled triangle. The distance from the bottom of the ladder to the wall acts as one of the sides (a), which is given as 5 ft. The length of the ladder itself acts as the hypotenuse (c), which is given as 12 ft.
Let's use the Pythagorean theorem to solve for the remaining side (b).
c^2 = a^2 + b^2
12^2 = 5^2 + b^2
144 = 25 + b^2
Now, subtract 25 from both sides to isolate b^2:
144 - 25 = b^2
119 = b^2
To solve for b, take the square root of both sides:
√119 ≈ 10.9
Therefore, the distance in feet from the ground that the ladder reaches the wall, rounded to the nearest tenth, is approximately 10.9 ft.