Question
Question 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 \( \angle \mathrm{E} \) ?
Ask by Conner Carrillo. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The tangent of angle E is 60 divided by 11, so tan E = 60 ⁄ 11.
Solution
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.
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution The Deep Dive
To find the tangent of \( \angle E \) in triangle \( \triangle EFG \), we utilize the definition of the tangent function in a right triangle, which is the ratio of the opposite side to the adjacent side. Here, \( EG \) is the opposite side to \( \angle E \), and \( GF \) is the adjacent side. Given: - \( EG = 11 \) - \( GF = 60 \) Thus, the ratio representing the tangent of \( \angle E \) can be calculated as follows: \[ \tan E = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{EG}{GF} = \frac{11}{60} \] So, the tangent of \( \angle E \) is \( \frac{11}{60} \).
