Question

find eg.
triangle image with right angle at g, angle at f is 66°, side ef is √66 (wait, maybe typo, maybe ef is length? wait, the triangle: vertices e, g, f, right angle at g, angle at f is 66°, side fg? wait, the text: write your answer as an integer or as a decimal rounded to the nearest tenth. eg = blank submit work it out

Explanation:

Step1: Identify triangle type and trigonometric ratio

We have a right - triangle \( \triangle EGF \) with \( \angle G = 90^{\circ} \), \( \angle F=66^{\circ} \), and hypotenuse \( EF = 66 \). We want to find the length of \( EG \), which is the side opposite to \( \angle F \). The sine of an angle in a right - triangle is defined as \( \sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}} \). So, \( \sin(\angle F)=\frac{EG}{EF} \).

Step2: Substitute values and calculate

We know that \( \angle F = 66^{\circ} \) and \( EF = 66 \). From the sine formula \( \sin(66^{\circ})=\frac{EG}{66} \). Then, we can solve for \( EG \) by multiplying both sides of the equation by 66: \( EG = 66\times\sin(66^{\circ}) \).

Using a calculator, \( \sin(66^{\circ})\approx0.9135 \). Then \( EG = 66\times0.9135 = 66\times0.9135 = 60.291\approx60.3 \) (rounded to the nearest tenth).

Answer:

\( 60.3 \)