Questions: Solve for the remaining angles and side of the one triangle that can be created. Round to the nearest hundredth: B=125°, c=3, b=6.5 C= A= a=

Solution Steps

To solve for the remaining angles and side of the triangle, we can use the Law of Sines and the fact that the sum of the angles in a triangle is 180 degrees. First, we can find angle $C$ using the Law of Sines, then find angle $A$ by subtracting the sum of angles $B$ and $C$ from 180 degrees. Finally, we can use the Law of Sines again to find side $a$.

We are given the following values for the triangle:

• $B = 125^\circ$
• $c = 3$
• $b = 6.5$

Using the Law of Sines, we can find angle $C$: $$\frac{c}{\sin C} = \frac{b}{\sin B}$$ Rearranging gives: $$\sin C = \frac{c \cdot \sin B}{b}$$ Substituting the known values: $$\sin C = \frac{3 \cdot \sin(125^\circ)}{6.5}$$ Calculating this yields: $$C \approx 22.21^\circ$$

Using the fact that the sum of angles in a triangle is $180^\circ$: $$A = 180^\circ - B - C$$ Substituting the values: $$A = 180^\circ - 125^\circ - 22.21^\circ \approx 32.79^\circ$$

Using the Law of Sines again to find side $a$: $$\frac{a}{\sin A} = \frac{b}{\sin B}$$ Rearranging gives: $$a = \frac{b \cdot \sin A}{\sin B}$$ Substituting the known values: $$a = \frac{6.5 \cdot \sin(32.79^\circ)}{\sin(125^\circ)} \approx 4.3$$

Final Answer