Answer:
The measure of angle F is 67.6°
Step-by-step explanation:
In the right triangle DEF
∵ ∠E is the right angle
∵ Side DF is opposite to ∠E
∴ DF is the hypotenuse of the triangle DEF
∵ Side EF is the adjacent side of ∠F
∵ The cosine ratio = [tex]\frac{Adjacent}{Hypotenuse}[/tex]
∴ cos∠F = [tex]\frac{EF}{DF}[/tex]
∵ EF = 8 units
∵ DF = 21 units
→ Substitute them in the cosine ratio above
∴ cos∠F = [tex]\frac{8}{21}[/tex]
→ Use [tex]cos^{-1}[/tex] to find the measure of angle F
∵ m∠F = [tex]cos^{-1}(\frac{8}{21})[/tex]
∴ m∠F = 67.60731219 degrees
→ Round it the nearest tenth of a degree
∴ m∠F = 67.6°
∴ The measure of angle F is 67.6°
