Question

A ladder of length 10m is leaning against a wall making an angle of 60° with the horizontal plane. It touches the wall at point A. If the ladder is rearranged in a way that it leans against the wall making an angle 30° with the horizontal plane, it touches the wall at point B. Find the length of AB.

Answer 1

Answer:

38.3 m

Step-by-step explanation:

Define x:

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)

Find the height of the wall when the ladder is 60º

sin θ = opp/hyp

sin (60) = x/10

x = 10 sin(60)

Find the height of the wall when the ladder is 30º

sin θ = opp/hyp

sin (30) = y/10

y = 10 sin 30

Find the height AB:

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

Answer: The height of AB is 38.3 m

Answer 2

HELLO DEAR,

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

the height AB is

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

I HOPE IT'S HELP YOU DEAR,

THANKS