Question

fall 2025 geometry ii wwva solving for angle measures of right triangles
determine the unknown angle measures of △def. round to the nearest degree.
m∠d = dropdown
m∠f = dropdown with 36, 44, 46, 54
diagram: right triangle def with right angle at e, de = 23.5, ef = 24.3, df = 33.8

Explanation:

Step1: Identify triangle type and sides

$\triangle DEF$ is right - angled at $E$. So, $DE = 23.5$, $EF=24.3$, and hypotenuse $DF = 33.8$. To find $\angle D$, we can use trigonometric ratios. The side opposite to $\angle D$ is $EF = 24.3$ and the side adjacent to $\angle D$ is $DE=23.5$. We can use the tangent function: $\tan(D)=\frac{\text{opposite}}{\text{adjacent}}=\frac{EF}{DE}$.
$\tan(D)=\frac{24.3}{23.5}\approx1.034$

Step2: Find the measure of $\angle D$

To find the angle whose tangent is approximately $1.034$, we use the inverse tangent function: $m\angle D=\arctan(1.034)$.
Using a calculator, $\arctan(1.034)\approx46^{\circ}$ (rounded to the nearest degree).

To find $\angle F$, we know that in a right - triangle, the sum of the non - right angles is $90^{\circ}$. So, $m\angle F = 90^{\circ}-m\angle D$. If $m\angle D\approx46^{\circ}$, then $m\angle F=90 - 46=44^{\circ}$.

Answer:

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