Find all solutions to the following triangle. (Round your answers for angles *A*, *C*, *A'*, and *C'* to the nearest whole number. Round your answers for sides *c* and *c'* to two decimal places. If either triangle is not possible, enter NONE in each corresponding answer blank.)

*B* = 118°, *b* = 0.65 cm, *a* = 0.97 cm

First triangle (assume *A* ≤ 90°):


  

To solve the given triangle, we are provided with the following information:

- \( B = 118^\circ \)
- \( b = 0.65 \) cm
- \( a = 0.97 \) cm

We'll use the Law of Sines to find angle \( A \):

\[
\frac{a}{\sin A} = \frac{b}{\sin B}
\]

Rearranging to solve for \( \sin A \):

\[
\sin A = \frac{a \cdot \sin B}{b}
\]

Substituting the values:

\[
\sin A = \frac{0.97 \cdot \sin 118^\circ}{0.65}
\]

Let's calculate \( \sin A \) and then find angle \( A \).It seems like I can’t do more advanced data analysis right now. Please try again later.

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Discover how to find all solutions to a triangle given angle B = 118°, side b = 0.65 cm, and side a = 0.97 cm using the Law of Sines. Round your answers for angles A, C, A', and C' to the nearest whole number, and for sides c and c' to two decimal places. If a triangle is not possible, 'NONE' will be provided for each corresponding answer blank. Suitable for high school students.

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