Two sectors have the same arc length. Their radii are r r\,r and 2r2r2r, and the angle of the larger sector is π3\displaystyle \frac{\pi}{3}3π radians less than the angle of the smaller sector. The sum of their areas is 27 cm2^22.
Find, in exact form, the two radii, the two angles and the common arc length.
221 exam-style questions on CCEA A Level Maths 3.4 Trigonometry (A-level only), covering 3.4.1 Trigonometry (A-level only), 3.4.2 Trigonometry (A-level only), 3.4.3 Trigonometry (A-level only), 3.4.4 Trigonometry (A-level only), 3.4.5 Trigonometry (A-level only), 3.4.6 Trigonometry (A-level only), 3.4.7 Trigonometry (A-level only), and 3.4.8 Trigonometry (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.