In a right triangle EFD, angle $F$ is the right angle, and the lengths of sides $EF$ and $FD$ are $3$ and $4$ units respectively. What is the measure of angle $EFD$ (in degrees)?

• A. $45$ degrees
• B. $36.87$ degrees
• C. $53.13$ degrees
• D. $60$ degrees

Answer: (C)

Verified step by step guidance

1. Identify the right triangle EFD with the right angle at vertex F, meaning \( \angle F = 90^\circ \). The sides given are \( EF = 3 \) units and \( FD = 4 \) units, which are the legs adjacent to the right angle.
2. Recall that the angle \( \angle EFD \) is the angle at vertex F between points E and D. Since \( F \) is the right angle, the angle \( \angle EFD \) is the right angle, so the problem likely asks for one of the other two angles, either \( \angle E \) or \( \angle D \). Here, we want to find \( \angle EFD \), which is the angle at vertex E opposite side FD or at vertex D opposite side EF.
3. Use the trigonometric ratios to find the measure of the angle at vertex E (or D). For example, to find \( \angle E \), use the tangent function, which relates the opposite side to the adjacent side: \[ \tan(\angle E) = \frac{FD}{EF} = \frac{4}{3} \].
4. Calculate the angle by taking the inverse tangent (arctangent) of the ratio: \[ \angle E = \tan^{-1}\left(\frac{4}{3}\right) \]. This will give the measure of \( \angle E \) in degrees.
5. Interpret the result as the measure of \( \angle EFD \) (or the angle at vertex E), which corresponds to approximately 53.13 degrees, confirming the correct answer.