Puzzle: The Mystery of the Triangle Heights

 A right triangle has one angle of 30° and a hypotenuse of length 10 units.

• Find the lengths of the other two sides using basic trigonometric functions.
• Find the height of the triangle (the perpendicular distance from the right angle to the hypotenuse).
• Bonus Challenge: If you were to inscribe a circle inside this triangle (called the incircle), what would be the radius of that circle?

Clues:

1. Hint for Side Lengths: Use the sine and cosine functions to find the sides opposite and adjacent to the 30° angle.
2. Hint for Height: Use the area formula for a triangle and relate it to the known base and height.
3. Hint for Bonus: The formula for the radius of the incircle is related to the triangle's area and perimeter.

Solve this puzzle step by step!