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 = °
2 answers:
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)
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