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