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Verified Answer :

Peytiii2829

Since we are asked to find DF, and we are given an angle and the side opposite to it, we can use the sine function to find DF.
let x be the length of side DF.

sin(32)= 17/x
x= 17 / sin(32)
x= 32.08

approximately 32.1

boffeemadrid

Answer:

(A) 32.1

Step-by-step explanation:

It is given that in ΔDEF, DE=17 and m∠F=32, thus

Using the trigonometry, we have

\(sinx=\frac{Perpendicular}{Hypotenuse}=\frac{DE}{DF}\)

⇒\(sin32^{\circ}=\frac{17}{DF}\)

⇒\(DF=\frac{17}{sin32^{\circ}}\)

⇒\(DF=\frac{17}{0.529}\)

⇒\(DF=32.1\)

Therefore, the value of DF is 32.1.

Hence option A is correct.

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