Two vertical poles are on either side of a road. A 30 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes angle 32° 24' with the pole and when it is turned to rest against another pole, it makes angle 32° 24' with the road. Calculate the width of the road.

Let AP and CQ be two poles.

When ladder is at position AB resting on pole AP.

Then, ∠BAP = 32° 24'

From figure,

In △ABP,

$\text{sin 32° 24}' = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}} \\[1em] \Rightarrow 0.536 = \dfrac{BP}{AB} \\[1em] \Rightarrow BP = AB \times 0.536 \\[1em] \Rightarrow BP = 30 \times 0.536 \\[1em] \Rightarrow BP = 16.08 \text{ meters}.$

When ladder is at position BC resting on pole CQ.

Then it makes angle 32° 24' with road.

∴ ∠CBQ = 32° 24'

From figure,

In △BQC,

$\text{cos 32° 24}' = \dfrac{\text{Base}}{\text{Hypotenuse}} \\[1em] \Rightarrow 0.844 = \dfrac{BQ}{BC} \\[1em] \Rightarrow BQ = BC \times 0.844 \\[1em] \Rightarrow BQ = 30 \times 0.844 \\[1em] \Rightarrow BQ = 25.32\text{ meters}.$

Width of road = BP + BQ = 16.08 + 25.32 = 41.4 meters.

Hence, width of road = 41.4 meters.