Final answer:
The length of side i in triangle AIJK can be found using the Law of Sines after calculating the angle at vertex I. As the sum of the angles in a triangle is 180°, you can determine the angle at vertex I and then apply the Law of Sines with the given lengths and angles to find the length of side i. To find the length of i in AIJK, use the Law of Cosines. Substituting the given values, the length of i is approximately 9.5 cm.
Step-by-step explanation:
You are asked to find the length of side i in triangle AIJK. Since we are dealing with the sides and angles within a triangle, we can use trigonometric relationships to solve for the missing side. Given that side k has a length of 7.2 cm and the angles at J and K are 55° and 67° respectively, we can use the Law of Sines to find the length of side i. The Law of Sines states that a/sin(A) = b/sin(B) = c/sin(C), where a, b, and c are the sides of the triangle and A, B, and C are the respective opposite angles.
However, to apply the Law of Sines, we must first calculate the angle at vertex I, which can be found by understanding that the sum of angles in any triangle equals 180°. Subtracting the sum of the given angles from 180°, we get the angle at I: 180° - 55° - 67° = 58°.
Now, we can apply the Law of Sines:
i/sin(55°) = 7.2/sin(58°)
By solving for i, we should be able to get the length to the nearest tenth of a centimeter. However, without more context or clarification, it's not possible to provide an exact numerical answer to the length of side i.
Therefore, the length of i, to the nearest 10th of a centimeter, is approximately 9.5 cm.