Brett has leaned a five-meter-long ladder against his house to paint a window. He placed the base of the ladder 3m away from the wall. How far up is the window?

think 3-4-5 right triangle

And in-case you don't know about 3,4,5 Pythagorean triples, the longest side of the triangle is the ladder (at 5 m) : )

It is the Pythagorean theorem (A^2+B^2=C^2) the C being the hypotenuse (5m) where a and b are the other two sides. You would get the equation (A^+9=25)then you subtract 9 from both sides(A^2=16) then you find the square root of 16 which is 4 (A= 4m)

To find out how far up the ladder the window is, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this scenario, the ladder forms the hypotenuse of a right-angled triangle, where the base of the ladder is one side and the distance up the wall to the window is the other side.

Step 1: Identify the given values:
The base of the ladder (one side of the triangle) is 3m.
The length of the ladder (the hypotenuse) is 5m.

Step 2: Use the Pythagorean theorem (a^2 + b^2 = c^2) to find the unknown side:
Let's call the distance up the wall to the window "x."
Using the formula, we get:
3^2 + x^2 = 5^2

Simplifying the equation:
9 + x^2 = 25

Step 3: Solve for x:
Subtract 9 from both sides:
x^2 = 25 - 9 = 16

To isolate x, take the square root of both sides:
x = √16 = 4

Therefore, the window is 4 meters above the ground.