Question

Triangle D E F is shown. Angle D E F is a right angle. The length of hypotenuse D F is 33.8, the length of D E is 23.5, and the length of E F is 24.3. Determine the unknown angle measures of △DEF. Round to the nearest degree. M∠D = ° m∠F = °

Answer 1

Answer:

MD is 46

MF is 44

Step-by-step explanation:

Answer 2

Answer:

m∠F = 44°

m∠D = 46°

Step-by-step explanation:

Find attached the diagram obtained from the information.

DE = 23.5, EF = 24.3, DF = 33.8

∠DEF = 90°

We are to determine ∠EDF = m∠D and ∠DFE =m∠F

Let ∠DFE =m∠F = x

∠EDF = m∠D = y

Using SOHCAHTOA, we would determine which of the trigonometry ratio would enable us find the angles.

To find x, we would apply tangent ratio

Tanx = opposite/adjacent

Tanx = 23.5/24.3

Tanx = 0.9671

x = arctan(0.9671)

x = 44.04

m∠F = x = 44° (nearest degree)

Let's determine the value of y

m∠F + m∠D + m∠E = 180(sum of angles in a triangle)

44° + y + 90° = 180°

134° + y = 180°

y = 180° - 134° = 46°

m∠D = y = 46° (nearest degree)