Triangle F G E is shown. Angle F E G is a right angle. The length of hypotenuse F G is 18.6 inches and the length of F E is 12 inches. Angle F G E is x. Which is the best approximation for the measure of angle EGF? 32.8° 40.2° 49.8° 57.2°

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.

Rewriting it in terms of x° as follows,

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,

Given that length of FE is 12 inch and FG is 18.6 inch.

Substituting the value,

To find the value of x, taking inverse sin.

Calculating the value,

Rounding to nearest tenth the value of angle is 40.2

Therefore measure of ∠FGE is 40.2° .

40.2 is correct

Step-by-step explanation: