Answer:
The measure of angle F is 67.6°
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 =

∴ cos∠F =

∵ EF = 8 units
∵ DF = 21 units
→ Substitute them in the cosine ratio above
∴ cos∠F =

→ Use
to find the measure of angle F
∵ m∠F =

∴ 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°