Question

sin(58°) =
c·sin(____°) = (4.25 / c)·c
c = 4.25 / sin(58°)

Explanation:

Step1: Analyze the sine law context

This problem relates to the Law of Sines in triangle trigonometry. The Law of Sines states that $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$ (where \(a,b,c\) are sides and \(A,B,C\) are opposite angles). Looking at the equation \(C\cdot\sin(\underline{\quad}^\circ)=\frac{4.25}{c}\cdot c\), simplify the right - hand side: \(\frac{4.25}{c}\cdot c = 4.25\). Also, from the first part \(\sin(58^{\circ})\) and the Law of Sines structure, the angle in the sine function should be \(58^{\circ}\) to be consistent with the Law of Sines setup (matching the angle for the side - angle relationship).

Step2: Confirm the angle value

The left - hand side is \(C\cdot\sin(\theta)\) and the right - hand side simplifies to \(4.25\). Given the first expression has \(\sin(58^{\circ})\), and the structure of the Law of Sines (where the angle should correspond to the angle opposite the side related to \(4.25\) and match the angle from \(\sin(58^{\circ})\)), the angle in the blank should be \(58\).

Answer:

The value in the blank is \(58\).