Solve each problem. (Source for Exercises 49 and 50: Parker, M., Editor, She Does Math, Mathematical Association of America.) Length of Sides of an Isosceles Triangle An isosceles triangle has a base of length 49.28 m. The angle opposite the base is 58.746°. Find the length of each of the two equal sides.

Key Concepts

Isosceles Triangle Properties

An isosceles triangle has at least two sides that are equal in length, and the angles opposite these sides are also equal. In this problem, the base is given, and the angle opposite the base is known, which allows us to use trigonometric principles to find the lengths of the equal sides.

Law of Cosines

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. It is particularly useful for non-right triangles, such as the isosceles triangle in this problem. The formula is c² = a² + b² - 2ab * cos(C), where C is the angle opposite side c.

Trigonometric Functions

Trigonometric functions, such as sine, cosine, and tangent, relate the angles of a triangle to the ratios of its sides. In this case, the cosine function will be used to find the lengths of the equal sides based on the known angle and the base length, facilitating the solution of the triangle.