Answer :

Answer: 51.1

Step-by-step explanation:

In the given picture , we have a right triangle Δ DEF right-angled at ∠F i.e. ∠ F= 90°.

Hypotenuse = DE = 9 units (Side opposite to right angle is hypotenuse)

[tex]\angle{E}=\theta[/tex]

and FD = 7 units

According to the trigonometry in a right triangle ,

[tex]\sin x=\dfrac{\text{Side opposite to x}}{\text{Hypotenuse}}[/tex]

In Δ DEF

So , [tex]\sin\theta=\dfrac{FD}{DE}[/tex]

[tex]\sin\theta=\dfrac{7}{9}\\\\ theta =\sin^{-1}(\dfrac{7}{9})\\\\=51.05755873\approx 51.1\ \ [\text{By using sin calculator.}]/tex]

Hence, the approximate value of θ is 51.1.

So the correct answer is "51.1".

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Rewritten by : Barada

Answer:

Step-by-step explanation:

[tex]sin \theta=\frac{7}{9}\\\theta=sin^{-1} (\frac{7}{9})\\\approx~ 51.1 ^\circ[/tex]