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

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

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

Answer

Explanation:

Step1: Identify the triangle type and sides

We have a right triangle ( \triangle EFG ) with right angle at ( G ). The hypotenuse ( EF = 8 ) and the opposite side to ( \angle F ) is ( EG = 3 ).

Step2: Use sine function

The sine of an angle in a right triangle is defined as ( \sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}} ). For ( \angle F ), ( \sin(\angle F)=\frac{EG}{EF}=\frac{3}{8} ).

Step3: Calculate the angle

To find ( \angle F ), we take the inverse sine (arcsin) of ( \frac{3}{8} ). So ( \angle F=\arcsin\left(\frac{3}{8}\right) ). Using a calculator, ( \arcsin\left(\frac{3}{8}\right)\approx22.0^\circ ) (rounded to the nearest tenth).

Answer:

( 22.0 )