Q.In a right-angled triangle, the difference between the two acute angles is 30°. Express the measures of those two angles in both radians and degrees.

In a right-angled triangle, the sum of the two acute angles is \(90^\circ\). Let the smaller angle be \(x^\circ\). ∴ The other angle is \((x + 30)^\circ\) So, \[ x + x + 30 = 90 \Rightarrow 2x + 30 = 90 \Rightarrow 2x = 60 \Rightarrow x = 30 \] ∴ The two angles are \(30^\circ\) and \((30 + 30)^\circ = 60^\circ\) We know that \(180^\circ = \pi\) radians ∴ \[ 30^\circ = \frac{\pi \times 30}{180} = \frac{\pi}{6} \text{ radians} \quad \text{and} \quad 60^\circ = \frac{\pi \times 60}{180} = \frac{\pi}{3} \text{ radians} \] ∴ The measures of the two angles are: - In radians: \(\frac{\pi}{6}\) and \(\frac{\pi}{3}\) - In degrees: \(30^\circ\) and \(60^\circ\)
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