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 =

Explanation:

Step1: Use tangent function for angle D

$\tan(D)=\frac{EF}{DE}=\frac{24.3}{23.5}$

Step2: Calculate angle D

$D = \arctan(\frac{24.3}{23.5})\approx46^{\circ}$

Step3: Use angle - sum property for angle F

In a right - triangle, $D + F+90^{\circ}=180^{\circ}$, so $F = 180^{\circ}-90^{\circ}-D$

Step4: Calculate angle F

$F=180^{\circ}-90^{\circ}-46^{\circ}=44^{\circ}$

Answer:

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