Why doesn't sine law work?

Joy

New member
"A person standing under a bridge finds that the angles of elevation to the ends of the bridge are 62 degrees and 71 degrees. If the distances from the ends of the bridge to the person are 420 m and 360 m, calculate the length of the bridge."

I realize you can solve this using cosine law. What I don't understand is why it won't work when I try to use sine law. Because of alternate angles, aren't the inside angles of the triangle 62 and 71 too?
So couldn't you solve it by doing sin62/360 = sin47/x?
But I tried that, and it didn't WORK, it was a different answer and there was another answer when I tried it with the other angle.

I am extremely confused.
Please help.
yeah, it's on deg
 
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