calculate the width of the road

Question

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

Answer 1

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

The diagram looks like this:

The total width of the road is given by

W = w1 + w2

where w1 = l.sin(alpha), and w2 = l.cos(alpha)

and l = 30 m and alpha = 32.4 degrees.

So, w1 = 30*sin(32.4) = 16.075 m,   and w2 = 30*cos(32.4) = 25.330 m

Giving W = w1 + w2 = 41.405 m

Width of road = 41.4 m

Answer 2

I assume the situation is that the foot of the ladder on the road stays in the same position when the ladder is resting on one or the other pole. Therefore 30sin32º24' is the distance of the foot from the first pole and 30cos32º24' is the distance of the foot from the second pole. The width of the road is the sum of these distances: 30(sin32º24'+cos32º24')=30*1.38015=41.40m approx.