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: Find \(m\angle D\)

Use the sine function: \(\sin D=\frac{\text{opposite}}{\text{hypotenuse}}\).
The side opposite \(\angle D\) is \(EF = 24.3\), and the hypotenuse \(DF=33.8\).
So, \(\sin D=\frac{24.3}{33.8}\).
Calculate \(\frac{24.3}{33.8}\approx0.72\).
Then, \(D=\sin^{- 1}(0.72)\).
Using a calculator, \(D\approx46^{\circ}\).

Step2: Find \(m\angle F\)

Since the sum of angles in a triangle is \(180^{\circ}\) and \(\angle E = 90^{\circ}\).
We know that \(m\angle D+m\angle F + 90^{\circ}=180^{\circ}\).
So, \(m\angle F=180^{\circ}-90^{\circ}-m\angle D\).
Substitute \(m\angle D = 46^{\circ}\), then \(m\angle F=180^{\circ}-90^{\circ}-46^{\circ}=44^{\circ}\).

Answer:

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