Question

Determine the unknown angle measures of ADEF.
Round to the nearest degree.
m2D
23.5
m2 =
24.3
D
33.8
F

Answer 1

Answer:

m∠D = 46°

m∠F = 44°

Step-by-step explanation:

cos D =base/hypo

cosD =23.5/33.8 = 0.695

so and D = 45.97°

thus angle F = 180-(90+45.97) =44.03°

Answer 2

Using relations in a right triangle, it is found that:

• The measure of angle D is of 46º.

• The measure of angle F is of 44º.

What are the relations in a right triangle?

The relations in a right triangle are given as follows:

• The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.

• The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.

• The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

In this problem:

• The hypotenuse is of 33.8.

• The side opposite to angle D is of 24.3.

• The side opposite to angle F is of 23.5.

Hence:

$\sin{D} = \frac{24.3}{33.8}$

$D = \sin^{-1}{\left(\frac{24.3}{33.8}\right)}$

$D = 46^\circ$

$\sin{F} = \frac{23.5}{33.8}$

$F = \sin^{-1}{\left(\frac{23.5}{33.8}\right)}$

$F = 44^\circ$

More can be learned about relations in a right triangle at https://brainly.com/question/26396675