Question #1fb7c

1 Answer
Nityananda
Nov 11, 2017

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)#]

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