if the hypotenuse of a right triangle is 8.1 the adjacent is 6.1 and the opposite angle is 5.8 what is the tan ratio?

The tan ratio is: tanθ = opposite/adjacent

Am I right to assume that instead of opposite angle you mean opposite side?

In which case . . .

Hyp: 8.1

Adj: 6.1

Opp: 5.8 

tanθ = 5.8/6.1

(I find SOHCAHTOA really useful to remember the ratios . . .  Sin = 0/H  Cos = A/H Tan = O/A)

If the two legs are 6.1 and 5.8  the hypotenuse is √[(6.1)^2 + (5.8)^2]  = √70.85  =  about 8.4

So

sine = opp/hyp   = 5.8/8.4

cos = adj/hyp = 6.1/8.4 

tan = 5.8 / 6.1

if the hypotenuse of a right triangle is 8.4 the adjacent is 6.1 and the opposite angle is 5.8 what is the tan ratio? i got 6.1 over 5.8 but the book says 5.8 over 8.4 

$$sin(A)=5.8/8.4$$

$$sin(B) =6.1/8.4$$

$$cos(A) = 6.1/8.4$$

$$cos(B) =5.8/8.4$$

$$tan(A)= 5.8/6.1$$

$$tan(B) = 6.1/5.8$$

The answer to your question is:  The tan ratio = 5.8/6.1!

But, if your book says that the ratio is 5.8/8.4 , then that MUST BE  the sine ratio, NOT the tangent!!!