Q) A ladder set against a wall at an angle 45° to the ground. If the foot of the ladder is pulled away from the wall through a distance of 4 m, its top slides a distance of 3 m down the wall making an angle 30° with the ground. Find the final height of the top of the ladder from the ground and length of the ladder.

Ans:  

(before we start, we should keep it in mind that we have to find height h and hence, we will convert all equation in h form…

Let’s start from ΔABC, sin 45⁰ =

(before we start, we should keep it in mind that we have to find height h and hence, we will convert all equation in h form…

Let’s start from ΔABC, Sin 45⁰ = 

• BC = (h+3) √2 ….. (i)

In ΔADE, Sin 30⁰ = 

• ED = 2h………..….. (ii)

We know that BC & ED both are the lengths of the ladder and equal.

Therefore, BC = ED

   (h+3) √2 = 2h

h =    = 3 (√2+1)

Hence, final height of the ladder’s top = 3 (√2+1) m

and length of ladder = 2 h

= 2 x 3(√2+1) m

Length of ladder =  6(√2+1) m