Question 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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Question 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 $$ \angle \mathrm{E} $$ ?

UpStudy AI · Accepted Answer

In right triangle $$ \triangle \mathrm{EFG} $$ with right angle at $$ \mathrm{G} $$, the sides are as follows:

- $$ \mathrm{EG} = 11 $$ (adjacent to $$ \angle \mathrm{E} $$)
- $$ \mathrm{GF} = 60 $$ (opposite to $$ \angle \mathrm{E} $$)
- $$ \mathrm{FE} = 61 $$ (hypotenuse)

The tangent of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. Therefore, for $$ \angle \mathrm{E} $$:

$$
\tan(\angle \mathrm{E}) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{\mathrm{GF}}{\mathrm{EG}} = \frac{60}{11}
$$

**Answer:** The ratio of tangent E is 60 divided by 11, that is
\tan E = 60 ⁄ 11.
The tangent of angle E is 60 divided by 11, so tan E = 60 ⁄ 11.

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