Question

I need help with number 3 please I need to get my grade up.

Answer 1

1. (correct) arccos
2. 47.3°
3. 20.57

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