Question

For the angles, a, b, and c in the triangle ABC is known that a : b : c = 2 : 1 : 3. AL is an angle divider and CD is the altitude. If CD = 18 cm what's the length of AL (in cm)?

Answer 1

Insufficient information is given to calculate the length of AL; the ratio of angles alone does not allow for determination of side lengths without additional geometric data.

Step-by-step explanation:

Calculating the length of AL in the triangle ABC given the ratio of the angles a : b : c = 2 : 1 : 3 and the altitude CD = 18 cm requires application of geometry and trigonometry. Since CD is the altitude and corresponds to 18 cm, there is not enough information to determine the length of AL directly. The provided ratio of the interior angles helps us understand the angle proportions, but without additional information, such as the length of the sides corresponding to these angles or the measure of any of the individual angles, we cannot calculate AL's length. Although we cannot find a solution, this exercise allows us to practice analytical thinking and understand the importance of complete geometric data when trying to solve a problem.