1. The problem asks to write \( \cos 66^\circ \) as a fraction using the right-angled triangle provided. 2. Recall that \( \cos \theta = \dfrac{\text{length of adjacent side}}{\text{length of hypotenuse}} \). 3. In the triangle, for the angle \(66^\circ\), the adjacent side length is given as 34 cm and the hypotenuse length is 37 cm. 4. Substitute these values into the cosine formula: $$ \cos 66^\circ = \dfrac{34}{37} $$ 5. This fraction represents \( \cos 66^\circ \) exactly for this triangle. Final answer: $$ \cos 66^\circ = \dfrac{34}{37} $$