In $$ riangle \mathrm{EFG} $$, the measure of $$ \angle \mathrm{G}=90^{\circ}, \mathrm{EG}=11, \mathrm{GF}=60 $$, and $$ \mathrm{FE}=61 $$. What ratio represents the tangent of $$ \angle \mathrm{E} $$ ?

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In $$ 	riangle \mathrm{EFG} $$, the measure of $$ \angle \mathrm{G}=90^{\circ}, \mathrm{EG}=11, \mathrm{GF}=60 $$, and $$ \mathrm{FE}=61 $$. What ratio represents the tangent of $$ \angle \mathrm{E} $$ ?

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In $$ \triangle \mathrm{EFG} $$, angle $$ \mathrm{G} $$ is the right angle ($$ 90^\circ $$). The sides are given as:
- $$ \mathrm{EG} = 11 $$
- $$ \mathrm{GF} = 60 $$
- $$ \mathrm{FE} = 61 $$

Since $$ \angle \mathrm{G} $$ is the right angle, the sides $$ \mathrm{EG} $$ and $$ \mathrm{GF} $$ are the legs of the triangle, and $$ \mathrm{FE} $$ is the hypotenuse.

To find $$ \tan(\angle \mathrm{E}) $$, we use the definition of tangent in a right triangle:
$$
\tan(\theta) = \frac{\text{Opposite side}}{\text{Adjacent side}}
$$
Here, for $$ \angle \mathrm{E} $$:
- The opposite side is $$ \mathrm{GF} = 60 $$
- The adjacent side is $$ \mathrm{EG} = 11 $$

Therefore:
$$
\tan(\angle \mathrm{E}) = \frac{60}{11} \quad \text{or} \quad 60:11
$$

**Answer:** The tangent of angle E is 60 to 11, that is, tan E = 60 : 11
The tangent of angle E is 60 to 11, or tan E = 60 : 11

In \( \triangle \mathrm{EFG} \), the measure of \( \angle \mathrm{G}=90^{\circ}, \mathrm{EG}=11, \mathrm{GF}=60 \), and \( \mathrm{FE}=61 \). What ratio represents the tangent of \( \angle \mathrm{E} \) ?

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