Lamp Wide Angle
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A hard trigonometry question...?
Could anybody please help me as to what the working out would be to answer this question? Thanks in advance:
A hedgehog wishes to cross a road without being run over. He observes the angle of elevation of a lamp post on the other side of the road to be 27 from the edge of the road and 15 from a point 10m back from the road. How wide is the road? If he can run 1m/s, how long will he take to cross?
Thanks
Let h = height of lamp post
Let x = width of road
tan(27) = h/x ....... so h = x*tan(27)
tan(15) = h/(x+10).... so h = (x+10)tan(15)
Then x*tan(27) = (x+10)tan(15)
x*tan(27) = x*tan(15) + 10*tan(15)
x[tan(27) - tan(15)] = 10*tan(15)
x = 10*tan(15) / [tan(27) - tan(15)]
x = 11.0917 meters
So if he runs at 1m/s, it takes (barely over) 11 seconds to cross the road.
I hope this helps!
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