Question

solve for x. round to the nearest tenth of a degree, if necessary.
triangle with right angle at f, gf=48, ge=60, angle at e is x degrees

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( EFG \), \( \angle F = 90^\circ \), hypotenuse \( EG = 60 \), adjacent side to \( \angle E \) (which is \( x^\circ \)) is \( EF \), and opposite side is \( FG = 48 \). Wait, actually, for angle \( E \), the adjacent side is \( EF \), opposite is \( FG = 48 \), hypotenuse \( EG = 60 \). So we can use sine: \( \sin(x) = \frac{\text{opposite}}{\text{hypotenuse}}=\frac{FG}{EG}=\frac{48}{60} \).

Step2: Calculate \( \sin(x) \)

Simplify \( \frac{48}{60} = 0.8 \). So \( \sin(x) = 0.8 \).

Step3: Find \( x \) using inverse sine

\( x = \arcsin(0.8) \). Using a calculator, \( \arcsin(0.8) \approx 53.1^\circ \) (rounded to the nearest tenth).

Answer:

\( 53.1^\circ \)