Answer :
To determine the value of [tex]\( n \)[/tex] to the nearest whole number using the Law of Cosines, follow these steps:
### Step-by-Step Solution:
1. Identify the formula and variables:
The Law of Cosines states:
[tex]\[ a^2 = b^2 + c^2 - 2bc \cos(A) \][/tex]
where [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] are sides of a triangle, and [tex]\( A \)[/tex] is the angle opposite side [tex]\( a \)[/tex].
2. Understand the given choices:
You need to determine which value of [tex]\( n \)[/tex] is most appropriate based on the provided choices: 18, 22, 29, and 41.
3. Apply the information:
Since the answer options are derived from considerations involving the Law of Cosines and the specific properties provided in the problem setup, the calculated or derived [tex]\( n \)[/tex] value is directly one of the given options.
4. Conclusion:
Comparing the values thus:
[tex]\[ n \approx 18 \quad \text{or} \quad n \approx 22 \quad \text{or} \quad n \approx 29 \quad \text{or} \quad n \approx 41 \][/tex]
The value of [tex]\( n \)[/tex] to the nearest whole number is among the given choices.
Therefore, the possible values for [tex]\( n \)[/tex] to the nearest whole number are: [tex]\([18, 22, 29, 41]\)[/tex].
This implies that one of these values correctly fits the requirement. Typically, further information or context such as specific sides or angles of a triangle would allow us to choose which exact solution is appropriate for the problem.
### Step-by-Step Solution:
1. Identify the formula and variables:
The Law of Cosines states:
[tex]\[ a^2 = b^2 + c^2 - 2bc \cos(A) \][/tex]
where [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] are sides of a triangle, and [tex]\( A \)[/tex] is the angle opposite side [tex]\( a \)[/tex].
2. Understand the given choices:
You need to determine which value of [tex]\( n \)[/tex] is most appropriate based on the provided choices: 18, 22, 29, and 41.
3. Apply the information:
Since the answer options are derived from considerations involving the Law of Cosines and the specific properties provided in the problem setup, the calculated or derived [tex]\( n \)[/tex] value is directly one of the given options.
4. Conclusion:
Comparing the values thus:
[tex]\[ n \approx 18 \quad \text{or} \quad n \approx 22 \quad \text{or} \quad n \approx 29 \quad \text{or} \quad n \approx 41 \][/tex]
The value of [tex]\( n \)[/tex] to the nearest whole number is among the given choices.
Therefore, the possible values for [tex]\( n \)[/tex] to the nearest whole number are: [tex]\([18, 22, 29, 41]\)[/tex].
This implies that one of these values correctly fits the requirement. Typically, further information or context such as specific sides or angles of a triangle would allow us to choose which exact solution is appropriate for the problem.
