Question

determining unknown angle measures of a right triangle
determine the unknown angle measures of △def.
round to the nearest degree.
m∠d =
°
m∠f =
23.5, 24.3, 33.8 are the side lengths of right triangle def with right angle at e.

Explanation:

Step1: Identify triangle type and sides

$\triangle DEF$ is a right triangle with $\angle E = 90^\circ$. Sides: $DE = 23.5$, $EF = 24.3$, $DF = 33.8$. To find $\angle D$ and $\angle F$, use trigonometric ratios (sine, cosine, tangent). Let's use tangent for $\angle D$: $\tan(\angle D) = \frac{EF}{DE} = \frac{24.3}{23.5}$.

Step2: Calculate $\angle D$

$\tan(\angle D) = \frac{24.3}{23.5} \approx 1.034$. Then $\angle D = \arctan(1.034) \approx 46^\circ$ (rounded). For $\angle F$, since triangle angles sum to $180^\circ$, $\angle F = 90^\circ - \angle D \approx 90 - 46 = 44^\circ$ (or use $\tan(\angle F) = \frac{DE}{EF} = \frac{23.5}{24.3} \approx 0.967$, $\angle F = \arctan(0.967) \approx 44^\circ$).

Answer:

$m\angle D = 46^\circ$, $m\angle F = 44^\circ$