If B is an obtuse angle and tan 2B = 24/7, find sin B

B = 143.13 degrees

sin (B) = sin (143.13) = 3/5 = 0.6

Step-by-step explanation:

Obtuse angles are the ones greater than 90 degrees but smaller than 180 degrees.

They belong to the second quadrant

We first find B'

tan (2*B') = 24/7

2*B' = arctan (24/7)

B' = 0.5*arctan (24/7)

B' = 36.869

But since B is from the second quadrant, this means that

B = 180 - B' = 143.13 degrees

sin (B) = sin (143.13) = 3/5 = 0.6