July 2015

Grazing cows


I was getting late for office; I opened the throttle and let my motorcycle fly.

But all my hopes of reaching office in time were dashed as I soon found myself at the tail of a traffic jam. The traffic snarl was caused by a herd of cows which was crossing the road at a leisurely pace. Nothing I could do about it. But the sight reminded me of a trigonometric problem I had come across recently. Here it is:

Three cows are tethered at each of the three corners of a triangular plot which is fenced all around so that the cows cannot cross its boundaries. The lengths of the sides of the triangular plot are 20 metres, 30 metres and 40 metres. The cows are tethered with ropes of 7-metre length each.

Please help me to find out the total area of the plot which can be grazed by the cows. Also please help me determine the area of the plot grazed by each cow.

Click here for the solution

Some useful links for
your career:

  • Union Public Service Commission - www.upsc.gov.in
  • IIT-Kharagpur - www.iitkgp.ac.in
  • Indian Statistical Institute - www.isical.ac.in
  • Indian Institute of Technology Madras - www.iitm.ac.in
  • Indian Institute of Management, Ahmedabad - www.iimahd.ernet.in
  • Indian Institute of Mass Commission - www.iimc.nic.in
  • IIT Bombay - www.iitb.ac.in
  • Indian School of Mines, Dhanbad - www.ismdhanbad.ac.in
  • Birla Institute of Technology, Ranchi - www.bitmesra.ac.in
  • Central Institute of Fisheries Nautical and Engineering Training - www.cifnet.nic.in
  • Indian Institute of Information Technology, Allahabad (Deemed University) - www.iiita.ac.in
  • Central Marine Fisheries Research Institute, Kochi - www.cmfri.com
  • Tata Institute of Social Sciences, Mumbai - www.tiss.edu

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