Question

express tan g as a fraction in simplest terms.

Explanation:

Step1: Recall tangent definition

For angle $G$, $\tan G = \frac{\text{opposite side}}{\text{adjacent side}}$ in right $\triangle GHI$.

Step2: Identify sides for $\angle G$

Opposite side to $G$ is $IH = 24$. First find adjacent side $GH$ using Pythagorean theorem:
$$GH = \sqrt{GI^2 - IH^2} = \sqrt{40^2 - 24^2} = \sqrt{1600 - 576} = \sqrt{1024} = 32$$

Step3: Compute $\tan G$

Substitute values into tangent formula:
$$\tan G = \frac{24}{32}$$

Step4: Simplify the fraction

Divide numerator and denominator by GCD 8:
$$\frac{24\div8}{32\div8} = \frac{3}{4}$$

Answer:

$\frac{3}{4}$