1.

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»

Let the base of wall be point O and top be point D.
Length of ladder(AD or BD) is 10 m.
If we draw a right angled ∆AOD:
angle DAO = 60°.
Using value of cos 60° = 1/2.
Cos 60° = AO/AD.
Putting all the values we get
1/2 = AO / 10 .
AO = 5m.
Similarly in ∆BOD
Cos 30° = OB/BD
Cos 30° = √3/2.
Putting all the values in the above equation:
√3/2 = OB/10.
OB = 5√3.
Distance between A and B = OB - OA = 5√3 - 5 = 5(√3 - 1) = 3.66 m.
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