In triangle DEFDEFDEF, ED=5cmED = 5\text{cm}ED=5cm and EF=6cmEF = 6\text{cm}EF=6cm. Given that cos(∠DEF)=53\displaystyle \cos(\angle DEF) = \frac{\sqrt{5}}{3}cos(∠DEF)=35 and ∠DEF \angle DEF\,∠DEF is acute.
Find the exact value of sin(∠DEF)\sin(\angle DEF)sin(∠DEF)
Find the length of DFDFDF, giving your answer to 3 significant figures.
Find ∠EFD\angle EFD∠EFD, giving your answer to 3 significant figures.
217 exam-style questions on Edexcel A Level Maths Trigonometric Ratios, covering 9.1 The Cosine Rule, 9.2 The Sine Rule, 9.3 Areas of Triangles, 9.4 Solving Triangle Problems, 9.5 Graphs of Sine, Cosine and Tangent, and 9.6 Transforming Trigonometric Graphs. Each one has a worked solution and a mark scheme showing where the marks go.