The boundary of a circular wildlife sanctuary is modeled by the equation x2+y2−14x+8y=175x^2 + y^2 - 14x + 8y = 175x2+y2−14x+8y=175, where distances are measured in kilometers.
A straight firebreak path connects two points A A\,A and B B\,B on the boundary. The angle subtended by the arc AB AB\,AB at the center of the sanctuary is 1.4 radians.
Calculate the area of the region bounded by the arc AB AB\,AB and the straight path ABABAB (the minor segment).
Give your answer to three significant figures.
317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.