Final answer:
To determine whether b or s is greater in an isosceles triangle with base angles that each measure 50 degrees, we can compare the heights of the triangle. The height opposite the 50-degree base angle is greater than the height opposite the 40-degree base angle, so b is greater than s.
Step-by-step explanation:
To determine whether b or s is greater in an isosceles triangle with base angles that each measure 50 degrees, we can use the trigonometric functions. Since an isosceles triangle has two congruent sides, the base angles are equal. In an isosceles triangle, the side opposite the base angle is also the height of the triangle. We can use the sine function to compare the heights of the triangle.
The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Since the triangles formed by the heights are similar, the heights can be compared by comparing the sine of the base angles.
In this case, since the base angles each measure 50 degrees, we can compare the sine of 50 degrees to the sine of any other angle less than 50 degrees. Since the sine function is increasing in the interval [0,90], we have sin(50) > sin(40). Therefore, the height opposite the 50-degree base angle is greater than the height opposite the 40-degree base angle, so b is greater than s.