Question

find ( mangle f ).

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

Explanation:

Step1: Identify sides relative to ∠F

In right triangle \( \triangle FEG \), for \( \angle F \):

• Opposite side: \( EG = 7 \)
• Hypotenuse: \( FG = 10 \)

Step2: Use sine function for ∠F

The sine of an angle in a right triangle is $\frac{\text{opposite}}{\text{hypotenuse}}$.
$\sin(\angle F) = \frac{7}{10} = 0.7$

Step3: Calculate ∠F with arcsine

Use inverse sine to find the angle measure:
$\angle F = \arcsin(0.7)$
Calculate the value using a calculator (ensure it is in degree mode):
$\angle F \approx 44.4^\circ$

Answer:

$44.4$