Question

find eg.
write your answer as an integer or as a decimal rounded to the nearest tenth.
eg =
submit

Explanation:

Step1: Identify the triangle type

We have a right - triangle \( \triangle EFG \) with \( \angle E = 90^{\circ} \), \( \angle G=54^{\circ} \) and \( EF = \sqrt{58} \). We want to find the length of \( EG \). We can use the tangent function in trigonometry. The tangent of an angle in a right - triangle is defined as the ratio of the opposite side to the adjacent side. For \( \angle G \), the opposite side is \( EF \) and the adjacent side is \( EG \). So, \( \tan(\angle G)=\frac{EF}{EG} \)

Step2: Solve for \( EG \)

We know that \( \tan(54^{\circ})\approx1.3764 \) and \( EF = \sqrt{58}\approx7.6158 \) (since \( \sqrt{58}\approx7.6158 \)). From the formula \( \tan(\angle G)=\frac{EF}{EG} \), we can re - arrange it to get \( EG=\frac{EF}{\tan(\angle G)} \)

Substitute the values of \( EF \) and \( \tan(54^{\circ}) \) into the formula: \( EG=\frac{\sqrt{58}}{\tan(54^{\circ})}\approx\frac{7.6158}{1.3764}\approx5.5 \)

Answer:

\( 5.5 \)