Question

find the sine, cosine, and tangent of ∠g. simplify your answers and write them as proper fractions, improper fractions, or whole numbers. sin (g) = cos (g) = tan (g) =

Explanation:

Step1: Find the hypotenuse \( EG \)

Using the Pythagorean theorem \( a^2 + b^2 = c^2 \), where \( a = 8 \), \( b = 6 \), and \( c = EG \).
\( EG^2 = 8^2 + 6^2 = 64 + 36 = 100 \), so \( EG = \sqrt{100} = 10 \).

Step2: Find \( \sin(G) \)

\( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \). For \( \angle G \), the opposite side is \( EF = 8 \), hypotenuse is \( EG = 10 \).
\( \sin(G) = \frac{8}{10} = \frac{4}{5} \).

Step3: Find \( \cos(G) \)

\( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \). For \( \angle G \), the adjacent side is \( FG = 6 \), hypotenuse is \( EG = 10 \).
\( \cos(G) = \frac{6}{10} = \frac{3}{5} \).

Step4: Find \( \tan(G) \)

\( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \). For \( \angle G \), the opposite side is \( EF = 8 \), adjacent side is \( FG = 6 \).
\( \tan(G) = \frac{8}{6} = \frac{4}{3} \).

Answer:

\( \sin(G) = \frac{4}{5} \)
\( \cos(G) = \frac{3}{5} \)
\( \tan(G) = \frac{4}{3} \)