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Weekly Challenge 5: Trigger

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

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Stadium Sightline

How would you design the tiering of seats in a stadium so that all spectators have a good view?

Weekly Challenge 3: Geometric Trig

Stage: 5 Short Challenge Level: Challenge Level:1

There are many ways to create the solution as it is something like a jigsaw. We used this method
 
1. Mark the right angles (use the fact the a radius and tangent at a point are at right angles)
2. Make all occurrences of the angle a
3. Mark the unit length
 
The diagram then becomes
 
 
To work out all of the areas we need to decide what unit of measurement the angle $a$ is in. Of course, we choose radians: there are $2\pi$ radians in a circle. We will also need to know the formula for the area of a circle and the area of a triangle. In this case, the areas are given as


The two largest areas are equal for around 0.40523 radians (23.2 degrees).