Final answer:
The ratio CL : AC is equal to the ratio of the lengths of the segments formed by the angle bisector BL. In this case, the ratio is 1 : 2.
Step-by-step explanation:
When BL is an angle bisector of ∠ABC, the ratio of CL : AC is equal to the ratio of the lengths of the segments formed by the angle bisector.
To find the ratio CL : AC, we can use the Angle Bisector Theorem, which states that the ratio of the lengths of two segments formed by an angle bisector is equal to the ratio of the lengths of the two sides of the triangle opposite the angle. In this case, the angle bisector BL divides the side AC into two segments: CL and AL.
Therefore, the ratio CL : AC is equal to the ratio of the lengths of the segments CL and AL, or CL : AL. Since BL is an angle bisector, the angles ∠ABC and ∠BAC are congruent. So, in triangle ABC, we have a 30°-60°-90° right triangle with AC as the hypotenuse and AL as the adjacent side.
Using the ratios of a 30°-60°-90° triangle, we know that the length of the adjacent side (AL) is half the length of the hypotenuse (AC). Therefore, the ratio CL : AC is 1 : 2.