Final answer:
To find the side length b in triangle ABC, we can use the Law of Sines. Using the given information: a = 8, sine of angle A = 2/7, and sine of angle B = 1/2. By setting up and solving the equation derived from the Law of Sines, we find that the side length b is 7.
Step-by-step explanation:
To find the side length b in triangle ABC, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is the same for all three sides of a triangle.
Using the given information, we have:
a = 8, sine of angle A = 2/7, and sine of angle B = 1/2.
Using the Law of Sines, we can set up the following equation:
b / sin(B) = a / sin(A)
Substituting the given values, we get:
b / (1/2) = 8 / (2/7)
Now, we can solve for b:
b = (1/2) * (8 / (2/7))
b = 7
Therefore, the side length b is 7.