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Geometric Trig

Age 16 to 18
ShortChallenge Level Yellow star
  • Problem
  • Getting Started
  • Solutions

This problem uses basic notions of trigonometry and areas of triangles which are fundamental to developments in A-level mathematics.
 
Being able to work with diagrams such as this is useful prepation for both coordinate geometry and mechanics.
 
 
 

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Degree Ceremony

Can you find the sum of the squared sine values?

Logosquares

Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.

Ball Bearings

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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