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In the diagram, the green triangle and the blue triangle are congruent, since they are both right-angled triangles with a 30$^\circ$ angle, and they share the side adjacent to the 30$^\circ$ angle.
The purple triangle is also a right-angled triangle with a 30$^\circ$ angle, but it is not congruent to the others, because the side it shares with the blue triangle is the hypotenuse of the blue triangle, but not of the purple triangle.
The green and blue triangles make an equilateral triangle:
This means that the side which the pink triangle shares with the blue triangle is 2 cm.
Then $x$ can be found using trigonometry:
$\cos{30} = \dfrac 2x $
$\Rightarrow x=\dfrac2{cos{30}}=\dfrac 4{\sqrt{3}}$
Three Right Angles
Age 14 to 16
ShortChallenge Level 
In the diagram, the green triangle and the blue triangle are congruent, since they are both right-angled triangles with a 30$^\circ$ angle, and they share the side adjacent to the 30$^\circ$ angle.The purple triangle is also a right-angled triangle with a 30$^\circ$ angle, but it is not congruent to the others, because the side it shares with the blue triangle is the hypotenuse of the blue triangle, but not of the purple triangle.
The green and blue triangles make an equilateral triangle:
This means that the side which the pink triangle shares with the blue triangle is 2 cm.
Then $x$ can be found using trigonometry:
$\cos{30} = \dfrac 2x $
$\Rightarrow x=\dfrac2{cos{30}}=\dfrac 4{\sqrt{3}}$
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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