Answer:
To find the angle between the equal sides of the triangle, we need to use the cosine rule, which states: c^2 = a^2 + b^2 - 2ab cos(C)
where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.
Let the lengths of the sides be 7x, 9x, and 9x, where x is a constant. Since the two equal sides are 9x each, we have:
c = 7x (opposite to the side of length 7x)
a = b = 9x (the two equal sides)
Substituting these values into the cosine rule, we get:
(7x)^2 = (9x)^2 + (9x)^2 - 2(9x)(9x)cos(C)
49x^2 = 162x^2 - 162x^2 cos(C)
cos(C) = (162x^2 - 49x^2) / (162x^2)
cos(C) = 113x^2 / 162x^2
cos(C) = 0.6975
C = cos^-1(0.6975)
C = 45.5 degrees (to the nearest degree)
Therefore, the angle between the equal sides is approximately 45 degrees