A ladder rest against a wall 7 m from the ground and distance from the foot of the ladder to the wall is 3 m. Compute for the length of the ladder.

To solve this problem, we can use the Pythagorean theorem because a ladder leaning against a wall forms 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 lengths of the other two sides. This can be written as: a² + b² = c².

Here, the height from the ground to where the ladder touches the wall is one side of the triangle (a = 7m), and the distance from the foot of the ladder to the wall is the other side (b = 3m). We want to find the length of the ladder, which is the hypotenuse (c).

Substituting the given values into the Pythagorean theorem gives us:

7² + 3² = c² 49 + 9 = c² 58 = c²

To find c, we take the square root of both sides:

c = sqrt(58) ≈ 7.62m

So, the length of the ladder is approximately 7.62 meters.