Question

Determine the unknown angle measures of △DEF. Round to the nearest degree. m∠D = ° m∠F = °

Answer 1

Angle D = 46
Angle F = 44

Answer 2

Answer:

$\angle F = 44\°\\\angle D= 46\°$

Step-by-step explanation:

The triangle that belongs to this exercise is attached.

As you can observe, the given triangle is a right triangle, that means we need to use trigonometric reasons to find its angles.

We know by definition that the angle E has 90°. So, we can apply the tangent reason to find angle F, as follows

$tan \angle F =\frac{23.5}{24.3}\\ \angle F = tan^{-1}(0.97) \approx 44\°$

Remember that the tangent of an angle is defined as the quotient between the opposite leg and the adjacent leg, which in this case are 23.5 and 24.3 respectively.

Now, to find angle D, we just neet to apply the internal angle theorem, which says that every triangle must be three angles that sum 180°, that is

$\angle D + \angle E + \angle F = 180\°\\\angle D + 90\° + \angle 44\° = 180\°\\\angle D = 180\° - 134\° = 46\°$

Therefore, the answers round to the nearet degree are,

$\angle F = 44\°\\\angle D= 46\°$