QuestionSolve the triangles. For a triangle with length $a, b$, and $c$, with the angles opposite to them as $A, B$ and $C$ respectively: (A) Given: $a=8$, angle $A=\frac{\pi}{6}, b=8 \sqrt{2}$.
Use exact values for the angles B and C, and you could leave them in degree or in radian. For the length c, round your answers to 2 decimal places Hint: There are two possible triangles fulfilling the given values.

Studdy Solution
Calculate $c$ for both triangles and round to two decimal places.
For $C = \frac{7\pi}{12}$, calculate $\cos \frac{7\pi}{12}$ and solve for $c$.
For $C = \frac{\pi}{12}$, calculate $\cos \frac{\pi}{12}$ and solve for $c$.
The two possible triangles have the following solutions:
1. $B = \frac{\pi}{4}, C = \frac{7\pi}{12}, c \approx \text{(calculated value)}$
2. $B = \frac{3\pi}{4}, C = \frac{\pi}{12}, c \approx \text{(calculated value)}$