Given a right triangle EGF with $\angle G$ as the right angle, if the side opposite $\angle E$ is $7$ units and the side adjacent to $\angle E$ is $9$ units, which is the best approximation for the measure of $\angle EGF$?

• A. $57.2°$
• B. $40.2°$
• C. $49.8°$
• D. $32.8°$

Answer: (B)

Verified step by step guidance

1. Identify the given information: In right triangle EGF, angle G is the right angle, the side opposite angle E is 7 units, and the side adjacent to angle E is 9 units.
2. Recall that the tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. So, \( \tan(\angle E) = \frac{\text{opposite}}{\text{adjacent}} = \frac{7}{9} \).
3. Use the inverse tangent function to find the measure of angle E: \( \angle E = \tan^{-1}\left(\frac{7}{9}\right) \).
4. Set up the calculation for \( \tan^{-1}\left(\frac{7}{9}\right) \) using a calculator or trigonometric tables to find the angle in degrees.
5. Compare the calculated angle to the given options (57.2°, 40.2°, 49.8°, 32.8°) to determine which is the best approximation for \( \angle E \).