find ( mangle g ).\n\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\n(…

find ( mangle g ).\n\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\n( mangle g = square^circ )

find ( mangle g ).\n\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\n( mangle g = square^circ )

Answer

Explanation:

Step1: Identify triangle type and trigonometric function

We have a right triangle ( \triangle EFG ) with ( \angle F = 90^\circ ), ( EF = 4 ), and ( EG = 6 ). To find ( m\angle G ), we can use the sine function, where ( \sin(\angle G)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{EF}{EG} ). ( \sin(\angle G)=\frac{4}{6}=\frac{2}{3} )

Step2: Solve for ( \angle G )

To find ( \angle G ), we take the inverse sine (arcsin) of ( \frac{2}{3} ). ( \angle G=\arcsin\left(\frac{2}{3}\right) ) Using a calculator, ( \arcsin\left(\frac{2}{3}\right)\approx 41.8^\circ )

Answer:

( 41.8 )