Answer: Choice A) 6.8 inches
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Step-by-step explanation:
It's a bit strange why your teacher has the "26 degree" label pointing at a side length, rather than an actual angle. I'm assuming your teacher meant to aim it at angle C. In other words, I'm assuming they meant to say angle C = 26 degrees.
If that assumption is correct, then,
A+B+C = 180
38+B+26 = 180
B+64 = 180
B = 180-64
B = 116
Then we can use the law of sines like so:
a/sin(A) = b/sin(B)
a/sin(38) = 10/sin(116)
a = sin(38)*10/sin(116)
a = 6.84986152123146
a = 6.8
Side 'a' is approximately 6.8 inches long. So that's why the answer is choice A.