Question

Need help trigonometry​

Answer 1

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 = $\frac{Adjacent}{Hypotenuse}$

∴ cos∠F = $\frac{EF}{DF}$

∵ EF = 8 units

∵ DF = 21 units

→ Substitute them in the cosine ratio above

∴ cos∠F = $\frac{8}{21}$

→ Use $cos^{-1}$ to find the measure of angle F

∵ m∠F = $cos^{-1}(\frac{8}{21})$

∴ 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°