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) = \boxed{} cos(g) = \boxed{} tan(g) = \boxed{}

Explanation:

Step1: Find the length of \( GE \)

In right triangle \( FEG \), by Pythagorean theorem \( FG^2 = FE^2 + GE^2 \). Given \( FG = 5 \), \( FE = 4 \), so \( GE = \sqrt{FG^2 - FE^2} = \sqrt{5^2 - 4^2} = \sqrt{25 - 16} = \sqrt{9} = 3 \).

Step2: Calculate \( \sin(G) \)

\( \sin(G) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{FE}{FG} = \frac{4}{5} \)

Step3: Calculate \( \cos(G) \)

\( \cos(G) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{GE}{FG} = \frac{3}{5} \)

Step4: Calculate \( \tan(G) \)

\( \tan(G) = \frac{\text{opposite}}{\text{adjacent}} = \frac{FE}{GE} = \frac{4}{3} \)

Answer:

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