Trigonometry - Basics of Trigonometric Ratios

A pentagon, \(ABCDE\), is made up of three triangles. Triangle \(ABC\) is congruent to triangle \(EDC\). \(AB = 9\text{ cm}\), \(CD = 12\text{ cm}\) and angle \(ABC\) and angle \(EDC = 90^\circ\).

1. Show that \(AC = 15\text{ cm}\).

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2. Giving your answer as a fraction in its simplest form, find \(\tan\angle ECD\).

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3. 1. Show that triangle \(ACE\) is a right-angled triangle.

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   2. Hence, find the shortest distance from \(C\) to \(AE\).

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