A sector of a circle has radius r r\,r cm and angle θ \theta\,θ radians, where 0<θ<π0 < \theta < \pi0<θ<π.
The perimeter of the sector is 20 cm and the area of the sector is 24 cm2^22.
Show that r r\,r satisfies the equation r2−10r+24=0r^2 - 10r + 24 = 0r2−10r+24=0.
Hence find the two possible pairs of values of r r\,r and θ\thetaθ.
State, with a reason, which of the two sectors has the longer arc.
317 exam-style questions on AQA A Level Maths 1.8 E: Trigonometry, covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context. Each one has a worked solution and a mark scheme showing where the marks go.