Question

In DEF DE=17 m angle =32 Find DF nearest tenth

Answer 1

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

Answer 2

(A) 32.1

Explanation:

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

Using the trigonometry, we have

`sinx=(Perpendicular)/(Hypotenuse)=(DE)/(DF)`

⇒
`sin32^(\circ)=(17)/(DF)`

⇒
`DF=(17)/(sin32^(\circ))`

⇒
`DF=(17)/(0.529)`

⇒
`DF=32.1`

Therefore, the value of DF is 32.1.

Hence option A is correct.