Two triangles can be formed using the given measurements. The other measurements of the triangle in which angle B is acute are also given. Solve the triangle in which angle B is obtuse.
Aequals=4444degrees°   aequals=99   bequals=1111
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Part 1
For the first​ triangle, the angle B is 58.158.1degrees°​, the measure of angle C is 77.977.9degrees°​, and the length of side c is 12.712.7.
Now consider the second triangle. The measure of angle B is enter your response heredegrees°.
​(Round to the nearest tenth as​ needed.)

To solve the triangle in which angle \( B \) is obtuse, we will use the Law of Sines and the information given for the triangle.

Given:
- \( A = 44^\circ \)
- \( a = 9 \)
- \( b = 11 \)

First, let's calculate angle \( B \) when it is acute using the Law of Sines:
\[ \frac{a}{\sin A} = \frac{b}{\sin B} \]

\[ \frac{9}{\sin 44^\circ} = \frac{11}{\sin B} \]

Solving for \(\sin B\):
\[ \sin B = \frac{11 \sin 44^\circ}{9} \]

Calculating \(\sin 44^\circ\) (using a calculator):
\[ \sin 44^\circ \approx 0.694 \]

Now, substituting the value:
\[ \sin B = \frac{11 \times 0.694}{9} \approx \frac{7.634}{9} \approx 0.848 \]

Therefore:
\[ B \approx \sin^{-1}(0.848) \approx 58.1^\circ \]

Given that there is a second triangle where \( B \) is obtuse, we calculate the obtuse angle by:
\[ B = 180^\circ - 58.1^\circ = 121.9^\circ \]

Now, we find the remaining angle \( C \):
\[ C = 180^\circ - A - B \]

For the obtuse triangle:
\[ C = 180^\circ - 44^\circ - 121.9^\circ = 14.1^\circ \]

Lastly, let's calculate the side \( c \) using the Law of Sines:
\[ \frac{c}{\sin C} = \frac{a}{\sin A} \]

Rearranging to solve for \( c \):
\[ c = \frac{a \cdot \sin C}{\sin A} \]

Substituting the known values:
\[ \sin C = \sin 14.1^\circ \approx 0.244 \]
\[ c = \frac{9 \cdot 0.244}{0.694} \approx 3.16 \]

So, the measurements for the triangle in which \( B \) is obtuse are:
- \( A = 44^\circ \)
- \( B = 121.9^\circ \)
- \( C = 14.1^\circ \)
- \( a = 9 \)
- \( b = 11 \)
- \( c = 3.2 \) (rounded to the nearest tenth)

Would you like more details or have any questions?

Here are some related questions to expand your understanding:

1. What is the Law of Sines and how is it used in solving triangles?
2. How do you determine if an angle in a triangle is obtuse or acute?
3. Can the Law of Cosines be used to solve this triangle? If so, how?
4. How would the solution differ if side \( a \) was longer than side \( b \)?
5. What are the properties of an obtuse triangle?
6. How do you calculate the area of a triangle given two sides and the included angle?
7. How can you verify the accuracy of your calculations in trigonometric problems?
8. What are some real-life applications of solving triangles?

**Tip:** When solving triangles using trigonometric functions, ensure your calculator is set to the correct mode (degrees or radians) based on the given angles.

Learn how to solve a triangle where angle B is obtuse using the Law of Sines. Given angle A, side lengths a and b, discover angle B and angle C. Detailed solution with step-by-step calculations.

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