The length of side AD is 6 cm.

<h3>Further explanation</h3>
We solve this problem using the principle of trigonometric ratio.
Look at the figure.
Given that the triangle ABC is right-angled at B
- Length of AB = 12 cm
- ∠ C = 30°
- The segment of BD is perpendicular to AC side.
We start from this statement:
“sum of measures of angles in a triangle is 180°.”
In the triangle ABC:
∠A + ∠B + ∠C = 180°
∠A + 90° + 30° = 180°
∠A + 120° = 180°
∠A = 180° - 120°
∠A = 60°
See the picture again. The triangle ABD is a right angle at D.
About angle D:
- AB is the hypotenuse
- AD is the adjacent side
Based on trigonometric ratios, the relationship between AD, AB, and angle A is as follows:





We get the length of AD is 6 cm.
<u>Note:</u>









<h3>Learn more</h3>
- Finding the value of sine of angle brainly.com/question/9610296
- Multiple choice about trigonometric ratios brainly.com/question/1445273
- Trigonometric identities brainly.com/question/1980819
Keywords: the length, side AD, right-angled, adjacent, hypotenuse, opposite, sin, cos, tan, sum of measures of angles in triangle are 180°, 30°, 60°