Question

tan(x) = 10/8

x = 45
x = 51.3
x = .02
x=80.2

Answer 1

We want x with tan x = 10/8 = 1.25.

Assuming x is in degrees:
- Principal solution: x = arctan(1.25) ≈ 51.34019175°.
- General solution: x = 51.34019175° + k·180°, k ∈ Z.
Checking your list (degrees):
- x = 45°: tan 45° = 1.00 (no)
- x = 51.3°: tan 51.3° ≈ 1.2482 (yes — very close to 1.25; 51.3° is an acceptable rounded value)
- x = 0.02°: tan ≈ 0.000349 (no)
- x = 80.2°: tan ≈ 5.79 (no)

If x is in radians:
- Principal solution: x = arctan(1.25) ≈ 0.89566479 rad, general x = 0.89566479 + k·π.
- None of 45, 51.3, 0.02, 80.2 (radians) are near those values, so none match in radians.

Tell me whether your x-values are in degrees or radians if you want further checks.