Question

Question #1fb7c

Answer 1

3.35 m (app)

Explanation:

Here Ladder formed hypotenuse with wall (height) and horizontal (base) with an angle of 60 degree. As per right angle triangle ;-
`sin 60^*` = height/hypotenuse = 3/hypotenuse.

`sqrt3/2` = 3/hypotenuse

Hypotenuse = 3 x 2/`sqrt3` = `2 sqrt3`

As the height of the ladder is fixed, means hypotenuse is fixed. But the ladder slides which formed 75 degree and touched new height of the wall.

Again `sin 75^*` = new height /hypotenuse.

`rArr [sqrt3+1]/(2sqrt2)` = new height/`2 sqrt3`

`rArr[2 sqrt3{sqrt3+1}]/(2 sqrt2)` = new height.

`rArr [1.732{1.732+1}]/1.414` = new height

So, new height = 3.35 m (app)

[NOTE : #sin 75^* = sin(45+30)^* = sin 45 cos 30 + cos 45 sin 30 = 1/sqrt2. sqrt3/2 + 1/sqrt2. 1/2 = [sqrt3 + 1]/(2 sqrt2)#]