If sin is .8 which is 4/5, that tells us that the opposite side is a length of 4 and the hypotenuse is a length of 5 (or at least a multiple of those).
If we are using a right triangle where a^2 +b^2 = c^2, we could find the missing side by filling in 4 for a and 5 for c.
- 4^2 + b^2 = 5^2
- 16 +b^2 = 25
- b^2 = 9 (Subtract 16 from both sides.)
- b = 3 (Take the square root of both sides.)
If b = 3 and b is the adjacent side, we have completed our triangle. Remember that tan X = opp/adj so tan X = 4/3. I would leave this as a fraction since it becomes a repeating decimal if you try to change it. Hope this helps!