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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