Question

express (sin g) as a fraction in simplest terms.

Explanation:

Step1: Identify the right triangle sides

In right triangle \( \triangle GHI \) with right angle at \( H \), \( GI = 20 \) (hypotenuse), \( GH = 16 \) (one leg), we first find \( HI \) using Pythagoras: \( HI=\sqrt{GI^{2}-GH^{2}}=\sqrt{20^{2}-16^{2}}=\sqrt{400 - 256}=\sqrt{144}=12 \).

Step2: Recall sine definition

Sine of an angle in a right triangle is \( \sin\theta=\frac{\text{opposite}}{\text{hypotenuse}} \). For \( \angle G \), opposite side is \( HI = 12 \), hypotenuse is \( GI = 20 \).

Step3: Simplify the fraction

\( \sin G=\frac{12}{20}=\frac{3}{5} \) (dividing numerator and denominator by 4).

Answer:

\( \frac{3}{5} \)