The base of a ladder leaning against a house is 30ft from the wall. if the ladder reaches 40ft high on the wall , how long is the ladder?

Since this forms a right-angle triangle, we can use the Pythagorean Theorem.

a^2 + b^2 = c^2

30^2 + 40^2 = c^2

900 + 1600 = c^2

2500 = c^2

50 = c

To determine the length of the ladder, we can use the Pythagorean Theorem, which states that the square of the hypotenuse (the longest side) of a right-angled triangle is equal to the sum of the squares of the other two sides.

In this case, the ladder represents the hypotenuse of a right-angled triangle, the wall represents one side, and the distance from the wall to the base of the ladder represents the other side.

Let's solve for the length of the ladder:

Step 1: Identify the values given in the problem:
- The distance from the base of the ladder to the wall: 30ft
- The height that the ladder reaches on the wall: 40ft

Step 2: Apply the Pythagorean Theorem:
Using the formula a^2 + b^2 = c^2, where a and b are the two shorter sides, and c is the hypotenuse (the ladder length in this case):

a^2 + b^2 = c^2

b = distance from the wall to the base of the ladder = 30ft
c = length of the ladder (unknown)
a = height that the ladder reaches on the wall = 40ft

Plugging in the values into the formula, we get:

30^2 + 40^2 = c^2
900 + 1600 = c^2
2500 = c^2

Step 3: Solve for c (length of the ladder):
To find the square root of 2500, we get:

c = √2500
c = 50ft

Therefore, the length of the ladder is 50ft.