Option A: 5 is the area of the triangle ABC
Explanation:
Given that ABC is a triangle.
Also, given that B = 45°, a = 10, and c = ![\sqrt{2}](/tpl/images/0539/5205/7e821.png)
We need to determine the area of the triangle ABC
The area of the triangle can be determined using the formula,
![Area=\frac{1}{2}ac\ Sin B](/tpl/images/0539/5205/3f036.png)
Substituting the values, we get,
![Area=\frac{1}{2}(10)(\sqrt{2}) \ Sin 45](/tpl/images/0539/5205/df1ee.png)
Substituting the value of Sin 45, we get,
![Area=\frac{1}{2}(10)(\sqrt{2}) (\frac{\sqrt{2} }{2} )](/tpl/images/0539/5205/186f8.png)
Multiplying, we have,
![Area=\frac{10\times2}{4}](/tpl/images/0539/5205/8f9f0.png)
Simplifying, we get,
![Area = 5](/tpl/images/0539/5205/7149c.png)
Thus, the area of the triangle ABC is 5
Therefore, Option A is the correct answer.