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

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

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

Answer

Explanation:

Step1: Identify triangle type and trigonometric ratio

This is a right triangle ( \triangle DEF ) with ( \angle F = 90^\circ ). We know the hypotenuse ( DE = 10.3 ) and the opposite side to ( \angle E ) is ( DF = 9.4 ). We use the sine function: ( \sin(\angle E)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{DF}{DE} ). [ \sin(\angle E)=\frac{9.4}{10.3} ]

Step2: Calculate the angle

To find ( \angle E ), we take the inverse sine (arcsin) of ( \frac{9.4}{10.3} ). [ \angle E=\arcsin\left(\frac{9.4}{10.3}\right) ] Using a calculator, ( \frac{9.4}{10.3}\approx0.9126 ), then ( \arcsin(0.9126)\approx65.9^\circ ) (rounded to the nearest tenth).

Answer:

( 65.9 )