Answer:
- (correct) arccos
- 47.3°
- 20.57
Step-by-step explanation:
1. The mnemonic SOH CAH TOA tells you the relationship between angle E and the given sides is ...
Cos = Adjacent/Hypotenuse
cos(E) = 19/28
E = arccos(19/28) . . . . the inverse cosine function is used
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2. E = arccos(19/28) ≈ 47.3°
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3. You can either use the Pythagorean theorem to find DF, or you can use the sine relation.
Sin = Opposite/Hypotenuse
sin(E) = DF/28
DF = 28·sin(E) = 28·sin(47.268°) . . . . original unrounded answer for E
DF ≈ 20.57
or ...
DF = √(DE² - EF²) = √(28² -19²) = √423 ≈ 20.56696...
DF ≈ 20.57
