Question

find eg.
triangle image with right angle at g, angle at f is 46°, side ef is 7
write your answer as an integer or as a decimal rounded to the nearest tenth.
eg =
submit

Explanation:

Step1: Identify triangle type and trigonometric ratio

We have a right - triangle \( \triangle EFG \) with \( \angle G = 90^{\circ} \), \( \angle F=46^{\circ} \), and \( EF = 7 \). We want to find the length of \( EG \). In a right - triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. For \( \angle F \), the opposite side is \( EG \) and the hypotenuse is \( EF \). So, \( \sin(\angle F)=\frac{EG}{EF} \).

Step2: Substitute values and solve for \( EG \)

We know that \( \angle F = 46^{\circ} \) and \( EF = 7 \). From the sine formula \( \sin(46^{\circ})=\frac{EG}{7} \). We can solve for \( EG \) by multiplying both sides of the equation by 7: \( EG = 7\times\sin(46^{\circ}) \).

Using a calculator, \( \sin(46^{\circ})\approx0.7193 \). Then \( EG=7\times0.7193 = 5.0351\approx5.0 \) (rounded to the nearest tenth).

Answer:

\( 5.0 \)