Question

A ladder leans against a wall making an angle of 45° with the ground. It reaches (√3-√2) m higher when the angle with the ground is made 60 degree. How long is the ladder?

Answer 1

let perpendicular be x, length of ladder=h
sin45=x/h
1/√2=x/h
h=√2x.......(I)
if height raise by √3-√2
sin60=x+√3-√2/h
√3/2=x+√3-√2/h
h=2/√3(x+√3-√2)......(ll)
equating both equation
√2x=2/√3(x+√3-√2)
√6x=2x+2√3-2√2
(√6-2)x = 2√3-2√2
x=2(√3-√2)/√6-2
rationalisation​
x= 2(√3-√2)(√6+2)/6-4
=2(3√2+2√3-2√3-2√2)
=2(√2-√3)
height of ladder=2√2(√2-√3)

Answer 2

Answer:

height of ladder=2√2(√2-√3)

Explanation

let perpendicular be x, length of ladder=h

sin45=x/h

1/√2=x/h

h=√2x...….(I)

if height raise by √3-√2

sin60=x+√3-√2/h

√3/2=x+√3-√2/h

h=2/√3(x+√3-√2)......(ll)

equating both equation

√2x=2/√3(x+√3-√2)

√6x=2x+2√3-2√2

(√6-2)x = 2√3-2√2

x=2(√3-√2)/√6-2

rationalisation​

x= 2(√3-√2)(√6+2)/6-4

=2(3√2+2√3-2√3-2√2)

=2(√2-√3)

height of ladder=2√2(√2-√3)