Question

Need help trigonometry
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Answer 1

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 =
`(Adjacent)/(Hypotenuse)`

∴ cos∠F =
`(EF)/(DF)`

∵ EF = 8 units

∵ DF = 21 units

→ Substitute them in the cosine ratio above

∴ cos∠F =
`(8)/(21)`

→ Use
`cos^(-1)` to find the measure of angle F

∵ m∠F =
`cos^(-1)((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°