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: Calculate hypotenuse $IG$

Use Pythagorean theorem:
$$IG=\sqrt{IH^2 + GH^2}=\sqrt{55^2 + 48^2}=\sqrt{3025+2304}=\sqrt{5329}=73$$

Step2: Find $\sin(G)$

Opposite over hypotenuse:
$$\sin(G)=\frac{IH}{IG}=\frac{55}{73}$$

Step3: Find $\cos(G)$

Adjacent over hypotenuse:
$$\cos(G)=\frac{GH}{IG}=\frac{48}{73}$$

Step4: Find $\tan(G)$

Opposite over adjacent:
$$\tan(G)=\frac{IH}{GH}=\frac{55}{48}$$

Answer:

$\sin(G)=\frac{55}{73}$, $\cos(G)=\frac{48}{73}$, $\tan(G)=\frac{55}{48}$