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".
