Final answer:
To find the height of the isosceles triangle, you can use the Pythagorean theorem. In this case, the height is approximately 8.31 inches.
Step-by-step explanation:
In an isosceles triangle, the base angles are congruent, which means that the sides opposite the base angles are also congruent. Therefore, in this triangle, the height can be considered as the perpendicular bisector of the base. To find the height, we can use the Pythagorean theorem.
Let's label the sides of the triangle: the base as b and the height as h. Since the sides are 20, 13, and 13 inches, the base b is 20 inches, and the other two sides are the same length, which means they are both 13 inches.
Using the Pythagorean theorem, we have 13² = h² + (b/2)². Plugging in the given values, we get 169 = h² + 10².
Solving for h, we find that the height of the isosceles triangle is √(169 - 100) = √69
= 8.31 inches.