Question 4 Using the Law of Sines to solve the all possible triangles if $\angle B=50^{\circ}, a=102, b=40$. If no answer exists, enter DNE for all answers. $\angle A$ is degreeß; $\angle C$ is degrees; \[ c= \] Assume $\angle A$ is opposite side $a, \angle B$ is opposite side $b$, and $\angle C$ is opposite side $c$ Question Help: Video Submit Question

Step 1 ：Use the Law of Sines to find \(\angle A\): \(\frac{a}{\sin A} = \frac{b}{\sin B}\)

Step 2 ：Rearrange for \(\sin A\): \(\sin A = \frac{a \sin B}{b}\)

Step 3 ：Substitute the given values: \(\sin A = \frac{102 \sin 50^\circ}{40}\)

Step 4 ：Calculate \(\sin A\) to get approximately 1.28

Step 5 ：Since the sine of an angle cannot be greater than 1, there are no possible triangles with the given measurements

Step 6 ：Therefore, \(\angle A\), \(\angle C\), and \(c\) are all DNE (Does Not Exist)

Step 7 ：\(\boxed{\text{DNE}}\)