A 13 feet ladder is placed 5 feet away from a wall. What is the distance from the ground straight up to the top of the ladder?
a^2 + b^2 = c^2
5^2 + b^2 = 13^1
25 + b^2 = 169
b^2 = 144
b = 12
ewan
To find the distance from the ground straight up to the top of the ladder, we can use the Pythagorean theorem. According to the theorem, in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder acts as the hypotenuse, and the distance from the ground straight up to the top of the ladder and the distance from the wall to the base of the ladder are the other two sides. Let's call the distance from the ground straight up to the top of the ladder "h" and the distance from the wall to the base of the ladder "b".
We have the following information:
- The ladder (hypotenuse) = 13 feet
- The distance from the wall to the base of the ladder (one of the legs) = 5 feet
According to the Pythagorean theorem:
(hypotenuse)^2 = (one leg)^2 + (other leg)^2
Substituting in the known values:
(13 feet)^2 = (5 feet)^2 + h^2
169 feet^2 = 25 feet^2 + h^2
Simplifying:
144 feet^2 = h^2
Taking the square root of both sides:
h = √144 feet
The distance from the ground straight up to the top of the ladder is 12 feet.
To find the distance from the ground straight up 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 (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder forms the hypotenuse of a right triangle, and the distance from the wall to the base of the ladder is one of the legs of the triangle.
Let's call the distance from the ground to the top of the ladder "x". We can use the Pythagorean theorem to set up the equation:
x^2 = 13^2 - 5^2
Simplifying the equation:
x^2 = 169 - 25
x^2 = 144
Taking the square root of both sides:
x = √144
x = 12
So, the distance from the ground straight up to the top of the ladder is 12 feet.