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Question

The difference between two acute angles of a right-angled triangle is $$ \dfrac{\pi}{9} $$. Find the angles in degrees.


Solution

$$ \pi $$ radians $$ = 180^{\circ} $$ 
$$ \dfrac{\pi}{9} $$ radian $$ = \dfrac{180}{\pi} \times \dfrac{\pi}{9} = 20^{\circ} $$ 

Let the two acute angles of the right-angled triangle be $$x$$ and $$y (x > y)$$ 
Then $$ x + y = 90^{\circ} $$         .............(i) 
and  $$x - y = 20^{\circ} $$            ...........(ii) 
Solving (i) and (ii) we get 
$$2x = 110^{\circ} $$ 
$$ \Rightarrow\ x = 55^{\circ} $$ 
$$55^{\circ} + y = 90^{\circ} \Rightarrow y = 35^{\circ} $$
Hence, two angles are $$55^{\circ} $$ and $$35^{\circ} $$ respectively.

Mathematics

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