Final answer:
To determine the size of angle θ in an isosceles triangle, additional information is required, such as the specific angle being referred to and whether the triangle is right-angled. With side lengths alone, we cannot calculate the angle without assuming extra details that were not provided.
Step-by-step explanation:
To calculate the size of angle θ (theta) in an isosceles triangle, where the lengths of the two equal sides are given as 5.9 and the base is 4.6, we can use the properties of isosceles triangles. Because the two sides are equal in length, the angles opposite these sides are also equal.
Without additional information about the location of angle θ, it's impossible to provide a definitive answer, as the triangle's apex angle and base angles cannot be determined with just the sides' lengths. Generally, if θ is the vertex angle, you would use the Law of Cosines to solve for the angle given the side lengths. If θ is one of the base angles, you could determine the vertex angle using the Law of Cosines and then calculate the base angle since the sum of angles in a triangle is always 180 degrees.
Notice that the description provided does not have all the necessary information to perform the calculation. If more context is provided such as which angle is θ (the vertex angle or a base angle), and if the triangle is right-angled, an accurate calculation can be made following the proper trigonometric approach.