Answer :
In an isosceles triangle, the two equal sides are opposite the two equal angles. To find the degree measure of the equal base angles, we can use the properties of isosceles triangles.
Let's denote the two equal sides of the isosceles triangle as a and the length of the base as b. In this case, the two equal sides are 66.9 inches long, and the base is 92.3 inches long.
By the property of isosceles triangles, the two equal base angles are congruent. Let's assume the degree measure of each equal base angle is x.
To find x, we can use the Law of Cosines, which states that for any triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the lengths of those sides and the cosine of the included angle.
Applying the Law of Cosines to our isosceles triangle, we have:
a^2 = b^2 + b^2 - 2(b)(b)cos(x)
Substituting the given values, we get:
(66.9)^2 = (92.3)^2 + (92.3)^2 - 2(92.3)(92.3)cos(x)
Simplifying and solving for cos(x), we find:
cos(x) = ((66.9)^2 - 2(92.3)^2) / (2(92.3)(92.3))
Taking the inverse cosine (cos^(-1)) of both sides, we can find the value of x in degrees.
Therefore, the degree measure of the two equal base angles can be calculated by finding the inverse cosine of the expression (((66.9)^2 - 2(92.3)^2) / (2(92.3)(92.3))) and converting the result to degrees using a calculator.
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