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 = [tex]\sqrt{2}[/tex]
We need to determine the area of the triangle ABC
The area of the triangle can be determined using the formula,
[tex]Area=\frac{1}{2}ac\ Sin B[/tex]
Substituting the values, we get,
[tex]Area=\frac{1}{2}(10)(\sqrt{2}) \ Sin 45[/tex]
Substituting the value of Sin 45, we get,
[tex]Area=\frac{1}{2}(10)(\sqrt{2}) (\frac{\sqrt{2} }{2} )[/tex]
Multiplying, we have,
[tex]Area=\frac{10\times2}{4}[/tex]
Simplifying, we get,
[tex]Area = 5[/tex]
Thus, the area of the triangle ABC is 5
Therefore, Option A is the correct answer.
