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# Puzzles

## Cutting corners

The diagram below shows a triangle $$ABC$$. The line $$CE$$ is perpendicular to $$AB$$ and the line $$AD$$ is perpedicular to $$BC$$.
The side $$AC$$ is 6.5cm long and the lines $$CE$$ and $$AD$$ are 5.6cm and 6.0cm respectively.
How long are the other two sides of the triangle?

## Equal side and angle

In the diagram shown, the lengths $$AD = CD$$ and the angles $$ABD=CBD$$.
Prove that the lengths $$AB=BC$$.

## Arctan

Prove that $$\arctan(1)+\arctan(2)+\arctan(3)=\pi$$.

## Sine

A sine curve can be created with five people by giving the following instructions to the five people:
A. Stand on the spot.
B. Walk around A in a circle, holding this string to keep you the same distance away.
C. Stay in line with B, staying on this line.
D. Walk in a straight line perpendicular to C's line.
E. Stay in line with C and D. E will trace the path of a sine curve as shown here:
What instructions could you give to five people to trace a cos(ine) curve?
What instructions could you give to five people to trace a tan(gent) curve?

## arccos + arcsin

What is the value of $$\arccos(x) + \arcsin(x)$$?

## Archive

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