Question

A ladder of height hcm is placed against a vertical wall. If the bottom of the ladder is 50cm from the base of the wall and the top of the ladder touches the wall at a height of 120cm, find h. Enter your next step here View next step

Answer 1

To find the length of the ladder, which is 50cm away from the wall and reaches up to 120cm on the wall, we can apply the Pythagorean theorem. The length of the ladder, which is the hypotenuse, is found to be 130cm.

Step-by-step explanation:

To find the length of a ladder that is leaning against a wall we can apply the Pythagorean theorem. The ladder, the wall, and the ground form a right-angled triangle. The vertical wall forms one side of this triangle (height), the ground represents the base, and the ladder itself is the hypotenuse.

Given that the bottom of the ladder is 50cm away from the wall (the base of the triangle), and the top of the ladder touches the wall at a height of 120cm (the other side of the triangle), we want to find the length of the ladder (the hypotenuse).

Applying the Pythagorean theorem (a2 + b2 = c2), where c is the hypotenuse and a and b are the other two sides of the triangle, we get:

502 + 1202 = h2

h = √(502 + 1202)

h = √(2500 + 14400)

h = √(16900)

h = 130cm

Therefore, the length of the ladder is 130cm.