(Solved): 2. Consider the two right triangles show in Figure 1, which share a side of length \( c \). The var ...

2. Consider the two right triangles show in Figure 1, which share a side of length \( c \). The variable \( b \) refers to the combined length of the bottom sides, and \( \theta \) is the indicated angle. The figure is not drawn to scale. Since the figure is not drawn to scale, you cannot assume that side \( b \) is split in half by the two triangles. (a) Solve algebraically for the unknown length \( x \) in terms of the known quantities \( \theta, b \), and \( c \) only. (Hint: Often when you solve math problems you will need to make up additional algebraic variables to help you write down useful equations. However, your final result should only contain the variables that were given.) \( x=\sqrt{C^{2}+b^{2}} \) (b) Now that you have a symbolic solution, you can plug numbers into that answer. If \( c=20, b=30 \), and \( \theta=40^{\circ} \), what is \( x \) ? Figure 1: Two right triangles that share a side. Not to scale.