Answer:
Measure of ∠FGE is 40.2°.
Step-by-step explanation:
Refer to the attachment.
Consider ΔFGE. Given that ∠FEG = 90° and ∠FGE is x°.
To find the value of ∠FGE use trigonometric ratios.
Use sine ratio to find the value of ∠FGE.
[tex]\sin \theta=\dfrac{opposite\:side}{hypotenuse\:side}[/tex]
Rewriting it in terms of x° as follows,
[tex]\sin x=\dfrac{opposite\:side}{hypotenuse\:side}[/tex]
Now find the opposite and hypotenuse side of the angle ∠FGE.
So opposite side of ∠FGE is FE and hypotenuse side of ∠FGE is FG.
Substituting the values,
[tex]\sin x=\dfrac{FE}{FG}[/tex]
Given that length of FE is 12 inch and FG is 18.6 inch.
Substituting the value,
[tex]\sin x=\dfrac{12}{18.6}[/tex]
To find the value of x, taking inverse sin.
[tex]x=\arcsin \left(\dfrac{12}{18.6}\right)[/tex]
Calculating the value,
[tex]x=40.17[/tex]
Rounding to nearest tenth the value of angle is 40.2
Therefore measure of ∠FGE is 40.2° .
