Attached _08Ask.png **Triangle Solution Using the Law of Sines****Problem Statement:**Use the Law of Sines to solve the triangle. Round your answers to two decimal places.\[ A = 100^\circ, \ a = 122, \ c = 14 \]**To Find:**\[ C = \,\,\,\,\,\,\,\,\,\,\,^\circ \]\[ B = \,\,\,\,\,\,\,\,\,\,\,^\circ \]\[ b = \,\,\,\,\,\,\,\,\,\,\, \]**Explanation:**The Law of Sines formula states that:\[\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\]Given:\[ A = 100^\circ \]\[ a = 122 \]\[ c = 14 \]**Step-by-Step Solution:**1. **Calculate Angle \(C\):** \[ \frac{122}{\sin(100^\circ)} = \frac{14}{\sin(C)} \] Solve for \(\sin(C)\): \[ \sin(C) = \sin(100^\circ) \times \frac{14}{122} \] Find \(\sin(100^\circ)\) using a calculator and proceed with the division and multiplication.2. **Calculate Angle \(B\):** Since the sum of angles in a triangle is always \(180^\circ\): \[ B = 180^\circ - A - C \]3. **Calculate Side \(b\):** Using the previously calculated angles: \[ \frac{b}{\sin(B)} = \frac{a}{\sin(A)} \] Solve for \(b\): \[ b = \frac{122 \times \sin(B)}{\sin(100^\circ)} \]Note: Use a scientific calculator to compute sine values and verify your calculations. Write down your answer for \(C\), \(B\), and \(b\) rounded to two decimal places.**Answer:**\[ C = \,\,\,\,\,\,\,\,\,\,\,^\circ \]\[ B = \,\,\,\,\,\,\,\,\,\,\,^\circ \]\[ b = \,\,\,

Name: Attached _08Ask.png **Triangle Solution Using the Law of Sines****Prob
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: Attached _08Ask.png **Triangle Solution Using the Law of Sines****Problem Statement:**Use the Law of Sines to solve the triangle. Round your answers to two decimal places.\[ A = 100^\circ, \ a = 122, \ c = 14 \]**To Find:**\[ C = \,\,\,\,\,\,\,\,\,\,