Final answer:
The question features an isosceles triangle with angles of 55°, 55°, and 70°, and the side opposite the 70° angle is 10 inches. To find the length of the other sides, we must use the Law of Sines. There is a typo in the given angles, as there is no 80° angle in the described triangle.
Step-by-step explanation:
The question contains an error regarding the angles of the isosceles triangle, but assuming the triangle is indeed isosceles with two angles of 55° each, and a third angle of 70°, the side across from the 70° angle will be of a different length than the other two, equal sides. Use the properties of isosceles triangles, which have two equal sides and two equal angles opposite those sides.
Since we know the angle that is not 55° is 70°, the sides opposite the 55° angles will be equal due to the properties of an isosceles triangle. The side mentioned as opposite the 80° angle (which does not exist in this triangle) cannot be 10 inches. However, assuming it refers to the side opposite the 70° angle, we can use the Law of Sines to find the lengths of the remaining sides.
The formula for the Law of Sines is a/sin(A) = b/sin(B) = c/sin(C), where a, b, and c represent the sides of the triangle, and A, B, and C represent the opposite angles. We can set up a ratio comparing the known side to its opposite angle, and equate it to the unknown side (let's call it x) and its opposite angle of 55°:
x/sin(55°) = 10/sin(70°)
By cross-multiplying and solving for x, we will find the length of the other two sides of the isosceles triangle. Since both sides opposite the 55° angles are equal, once we find x, both sides will be of this same length.