https://file.aiquickdraw.com/mathbot/file/1726533006307gix9o2k6.jpg

It looks like you have uploaded an image of a right triangle and you are asked to find the missing sides. The triangle seems to involve a specific angle and some known side lengths, making it a special right triangle problem.

Based on the image:
- One angle is given as \( 30^\circ \) (from the angle marked at \( A \)).
- The side opposite the \( 30^\circ \) angle (side \( AC \)) is 6 units.
- Side \( AB \) is the hypotenuse, and side \( BC \) is adjacent to the \( 30^\circ \) angle.

This is a 30-60-90 special right triangle, where the sides have the following ratio:
- Opposite the \( 30^\circ \) angle: \( x \),
- Opposite the \( 60^\circ \) angle: \( x \sqrt{3} \),
- Hypotenuse: \( 2x \).

Given that the side opposite the \( 30^\circ \) angle (side \( AC \)) is 6, we can deduce that:
- \( AC = x = 6 \),
- The hypotenuse \( AB = 2x = 2 \times 6 = 12 \),
- The other leg \( BC = x \sqrt{3} = 6 \sqrt{3} \).

### Solution:
- The length of side \( BC \) is \( 6\sqrt{3} \).
- The length of side \( AB \) is \( 12 \).

Would you like more details on the solution, or have any further questions?

Here are 5 related questions to consider:
1. How do the ratios in a 30-60-90 triangle compare to a 45-45-90 triangle?
2. How would the solution change if \( AC \) were doubled?
3. Can the Pythagorean theorem be used to verify the lengths of the sides?
4. What are some real-life applications of special right triangles?
5. How do you calculate the area of this triangle using the known side lengths?

**Tip:** When solving problems involving special right triangles, memorize the side ratios to solve quickly without needing extensive calculations.

Find the missing sides of the special right triangle, where AC = 6 and the angle at A is 30 degrees.

Solve a 30-60-90 triangle where AC = 6 and the angle at A is 30°. Learn how to find the missing sides using the 30-60-90 triangle theorem and apply the ratios of x, x√3, and 2x. This problem is suitable for students in Grades 9-11.

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