Hello! :)
[tex]\large\boxed{x \approx 7.064}}[/tex]
In the diagram, we are given the opposite side of ∠A as 8.
We are trying to solve for the adjacent side, so we must use the appropriate trig.
Cotangent uses both the adjacent and opposite sides, so we can use this to find the value of x.
Cot (angle) = Adjacent / Opposite, therefore:
cot (28°) = x / 8
Multiply both sides by 8 to isolate for x:
8 · cos(28°) = x
Evalute cos(28°) using a calculator:
cos(28°) ≈ 0.88295
Multiply by 8 to solve for x:
8 · cos(28°) ≈ 7.064
