This is one of the difficult question from trigonometry (height and distance) in which we are to find the length of the ladder when an electrician has to repair an electric fault on a pole of height 4m. He needs to reach a point 1m below the top of the pole to undertake the repair work. What should be the length of the ladder that she should use which, when inclined at an angle of 60° to the horizontal, would enable her to reach.

RS Aggarwal, class 10, chapter 14, question no 32

## Let AC be the electricpole of height 4 m. Let B be a point 1.3 m below the top A of the pole AC.

Then, BC = AC – AB = (4 – 1.3)m = 2.7 m

Let BD be the inclined at an angle of 60∘ to the horizontal.

In ΔBCD, we have

sin60∘=BC/BD

⇒√3/2=2.7/BD [∵BC=2.7m]

⇒BD=(2×2.7m)/√3=5.4/√3m=5.4×√3/3m

⇒BD=(1.8)√3m=9/5√3m

Hence, the length of the ladder should be 9√3/5m.