To find the length of AE in the given figure, we can use trigonometry and the information provided.
Given:
- AB = 20 units
- Angle A = 30°
We need to use trigonometric ratios to find the length of AE. Since we have the angle and the side adjacent to it (AB), we can use the cosine function.
\[ \cos(\text{angle}) = \frac{\text{adjacent side}}{\text{hypotenuse}} \]
In this case, the adjacent side is AB and the hypotenuse would be AC. To find AC, we can use the cosine function:
\[ \cos(30°) = \frac{AB}{AC} \]
\[ \cos(30°) = \frac{20}{AC} \]
Since the cosine of 30° is \( \frac{\sqrt{3}}{2} \), we can substitute this value into the equation:
\[ \frac{\sqrt{3}}{2} = \frac{20}{AC} \]
Now, we can solve for AC:
\[ AC = \frac{20}{\frac{\sqrt{3}}{2}} \]
\[ AC = \frac{20 \times 2}{\sqrt{3}} \]
\[ AC = \frac{40}{\sqrt{3}} \]
\[ AC = \frac{40\sqrt{3}}{3} \]
Therefore, the length of AC is \( \frac{40\sqrt{3}}{3} \) units.
