Use the law of sines to solve the​ triangle, if possible.
cequals8 ​mi, Bequals39.78degrees​, Cequals32.49degrees
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Part 1
Find the measure of angle A. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
Aequals
  
enter your response heredegrees ​(Type an integer or a​ decimal.)
B.
There is no solution.


To solve the triangle using the Law of Sines, we start by finding the measure of angle \( A \).

First, we use the fact that the sum of the angles in a triangle is always 180 degrees:
\[ A + B + C = 180^\circ \]

Given:
\[ B = 39.78^\circ \]
\[ C = 32.49^\circ \]

We can find \( A \) by subtracting the sum of \( B \) and \( C \) from 180 degrees:
\[ A = 180^\circ - B - C \]
\[ A = 180^\circ - 39.78^\circ - 32.49^\circ \]
\[ A = 180^\circ - 72.27^\circ \]
\[ A = 107.73^\circ \]

Therefore, the measure of angle \( A \) is:
\[ A = 107.73^\circ \]

So the correct choice is:
A. \( A = 107.73 \) degrees

Would you like the detailed steps for finding the lengths of the other sides using the Law of Sines, or do you have any other questions?

Here are 5 questions you might consider asking:
1. How do you use the Law of Sines to find the length of side \( a \)?
2. Can you explain the Law of Cosines and when to use it?
3. What is the formula for the Law of Sines?
4. How do you solve a triangle given two sides and an included angle?
5. What are the possible scenarios for the number of solutions in a triangle problem?

**Tip:** Always double-check your angle measures to ensure they sum to 180 degrees in a triangle.

Learn how to solve a triangle using the Law of Sines with given angle and side measurements. This problem involves calculating the measure of angle A in a triangle with sides and angles provided. Suitable for high school students studying trigonometry and geometry.

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