Complete the table by using the names of the sides to express each trigonometric function as a ratio. \( \sin B=\frac{b}{c} \) \( \cos B=\frac{a}{c} \) \( \tan B=\frac{b}{a} \) The unknown side length \( b \) is \( \square \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) sec \( B=\frac{c}{b} \) cot \( B=\frac{a}{b} \) n

To find the unknown side length \( b \) using trigonometric functions, you can use the definitions you’ve provided. Since \( \sin B = \frac{b}{c} \) implies \( b = c \cdot \sin B \), if you know the hypotenuse \( c \) and angle \( B \), you can easily calculate \( b \). If you're working with specific angle values, don't forget to convert them into radians or degrees as appropriate for your calculations! For example, if \( B = 30^\circ \), then \( b = c \cdot \sin(30^\circ) = \frac{c}{2} \) if \( c \) is the hypotenuse. Remember, it's always helpful to visualize these functions on the unit circle for a deeper understanding!