Question

A ladder of length 10 m 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.

please guys give me fast and full answer

Answer 1

From triangle ACD we get,

sin 60 degree = AC/10

or, (3^1/2)/2 = AC/10

or, AC = 5 x (3^1/2) metre.

Similarly, from triangle BCE we get,

sin 30 degree = BC/10

or, 1/2 = BC/10

or, BC = 5metre.

Now we know that AB = AC - BC = 5 x (3^1/2) metre - 5 metre.

= 5(root3 - 1) metre. (Ans).

Answer 2

SIN60°=L/H

L=AC

H=10

AC/10= √3/2

AC=5√3 meter

And

Sin30° = L"/H

L"= BC

H=10

BC/10=1/2

BC=5 cm

So

AB= AC-BC

= 5√3-5

=5(√3-1) meter