a ladder is 9 meter tall.it is inclined on a wall and reaches 7 meter.what is the distance of its base from the wall

The ladder forms a triangle with the wall and the ground. The three points of the triangle are (a) at the foot of the ladder, (b) at the base of the wall, and (c) where the top of the ladder touches the wall; the three sides are the ladder itself, the distance on the ground from the foot of the ladder, and the distance up the wall from the ground to the top of the ladder. The ground and the wall form a right angle, so the triangle is right, and since the ladder is opposite the right angle, it forms the hypotenuse.

The Pythagorean Theorem tells us that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.

a²+b²=c²

Here, we know the length of one side (the distance up the wall to the top of the ladder) and the hypotenuse (the ladder). We have to solve for the unknown side.

7²+b²=9²

49+b²=81

(49+b²)-49=81-49

b²=32

√(b²) = √(32)

b = √(16×2)

b = √(16)×√(2)

b = 4×√(2)

b ≈ 5.7m