Answer: The tangent ratio for angle E is [tex]\dfrac{3}{4}.[/tex]
Step-by-step explanation: We are given to find the tangent ratio of angle E in the figure.
From the figure, we note that
the triangle DEF is a right-angled triangle, where ∠D = 90° and ∠E is an acute angle.
We know that
tangent ratio of an angle is given by the length of the perpendicular divided by the length of the base associated with that particular angle.
Now, for angle E, we have
perpendicular = DF = 6 units
and
base = DE = 8 units.
Therefore, the tangent ratio for angle E will be
[tex]\tan \angle E=\dfrac{perpendicular}{base}\\\\\\\Rightarrow \tan \angle E=\dfrac{DF}{DE}\\\\\\\Rightarrow \tan \angle E=\dfrac{6}{8}\\\\\\\Rightarrow \tan \angle E=\dfrac{3}{4}.[/tex]
Thus, the tangent ratio for angle E is [tex]\dfrac{3}{4}.[/tex]
