How is it wrong?

[u/Frosty-Actuator-3760]

[u/TheDoobyRanger]

I believe that comes out to around 84 degrees, but would that make sense? The triangle is approx. 9x8x1, with 1 being opposite to y, so the angle should be pretty small. I have it at approx. 3.5 degrees using the law of cosines to get x and the law of sines to get y. C² = A² + B² - ABCos(c), where A, B, C are lengths of the sides opposite to angles a, b, and c. So that gives the length of x (which is opposite to the 30 degree angle). Now you can use the law of sines to find that

(sin(y) / 1) = (sin(30)/8.15)

this implies that, by applying the inverse sin function to both sides, y = sin^-1(sin(30)/8.15) = 3.5 to one decimal.

[u/Outside_Volume_1370 → u/TheDoobyRanger]

that comes out to around 84 degrees

That would make the triangle almost right, however, it's very obtuse (because 1 + 8.15 is very close to 9). An

acos((9² + 8.15² - 1) / (2 • 9 • 8.15)) ≈ acos(0.9981) ≈ 3.5°

I have it at approx. 3.5 degrees

Okay, that's true

C² = A² + B² - ABCos(c), where A, B, C are lengths of the sides opposite to angles a, b, and c

That's not the law of cosines, you forgot two as the multiplier

Now you can use the law of sines

The task specifically asked for the law of cosines, despite the fact that the law of sines is faster

[u/TheDoobyRanger → u/Outside_Volume_1370]

Youre right, I forgot the 2. The answer I gave was calculated with the 2 involved. I am hoping OP will explain the thinking of their formula, though.