Question

A Ladder of Length 10m is leaning againts a wall making an angle 60⁰ with the horizontal plane. It touches the wall at point. If ladder is rearranged in a way that it leans against the wall making an angle 30⁰with horizontal,it touches the wall at point B. find the length of AB.​

Answer 1

Answer:

Length of AB is 38.3 m .

Step-by-step explanation:

Let the height of the wall from the ground to point A be x

The height of the wall from the ground to point B be y

Distance of AB = (x - y)

The height of the wall from ground to point A when the ladder is 60º

=> sin θ = opp/hyp

=> sin (60) = x/10

=> x = 10 sin(60)

The height of the wall from ground to point B when the ladder is 30º

=> sin θ = opp/hyp

=> sin (30) = y/10

=>y = 10 sin 30

height of AB = x - y

AB = 10 sin 60 - 10 sin 30

AB = 10( √3/2 - 1/2)

AB = 5(√3 - 1)

AB = 5√3 - 5 = 38.3 m