Final answer:
The measure of the included angle in the obtuse triangle is approximately 178.6°.
Step-by-step explanation:
To find the measure of the included angle in an obtuse triangle, we can use the Law of Cosines. The formula is: a^2 = b^2 + c^2 - 2bc*cos(A), where a, b, and c are the sides of the triangle and A is the included angle. In this case, we are given the side lengths of 10 and 26, and we are looking for the angle A. By substituting the values into the formula, we can solve for A.
a^2 = 10^2 + 26^2 - 2*10*26*cos(A)
a^2 = 100 + 676 - 520*cos(A)
a^2 = 776 - 520*cos(A)
93^2 = 776 - 520*cos(A)
8649 = 776 - 520*cos(A)
520*cos(A) = 776 - 8649
520*cos(A) = -7873
cos(A) = -7873/520
A = cos^(-1)(-7873/520)
A ≈ 178.6°