Question

find:
the figure is not drawn to scale.
answer
$\frac{24}{30}$
$\frac{18}{30}$
$\frac{24}{18}$
$\frac{18}{24}$

Explanation:

Step1: Identify the sides relative to angle A

In a right triangle, for angle A, the opposite side is 24, the adjacent side is 18, and the hypotenuse is 30. We need to find the ratio related to angle A (probably sine, cosine, or tangent). Let's check the options. The options are fractions. Let's recall trigonometric ratios: $\sin A=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan A=\frac{\text{opposite}}{\text{adjacent}}$. Wait, the options: $\frac{24}{30}$, $\frac{18}{30}$, $\frac{24}{18}$, $\frac{18}{24}$. Let's see angle A: adjacent is 18, opposite is 24, hypotenuse 30. Wait, maybe it's $\cos B$ or $\sin A$? Wait, no, let's check the sides. Wait, the triangle has legs 18 and 24, hypotenuse 30. Let's check the options. The option $\frac{18}{24}$: wait, no. Wait, maybe it's the ratio of adjacent to opposite for angle A? No, wait, let's see the options. Wait, the last option is $\frac{18}{24}$? Wait, no, the fourth option is $\frac{18}{24}$? Wait, no, the user's image: the options are $\frac{24}{30}$, $\frac{18}{30}$, $\frac{24}{18}$, $\frac{18}{24}$. Wait, angle A: adjacent side is 18, opposite side is 24. So $\tan A=\frac{\text{opposite}}{\text{adjacent}}=\frac{24}{18}$, but that's one option. Wait, no, maybe it's $\cos A$? No, $\cos A=\frac{18}{30}$, $\sin A=\frac{24}{30}$. Wait, but the question is "Find" (probably $\tan A$ or something). Wait, no, maybe the question is about the ratio of the adjacent to the opposite for angle A? Wait, no, let's check the options. Wait, the fourth option is $\frac{18}{24}$, which is $\frac{\text{adjacent}}{\text{opposite}}$ for angle A. Wait, maybe the question is to find $\cot A$, which is $\frac{\text{adjacent}}{\text{opposite}}=\frac{18}{24}$. Let's check: $\cot A=\frac{\text{adjacent}}{\text{opposite}}=\frac{18}{24}$. So that's the fourth option. Wait, but let's confirm. The triangle: right angle, legs 18 (adjacent to A) and 24 (opposite to A), hypotenuse 30. So $\cot A = \frac{\text{adjacent}}{\text{opposite}}=\frac{18}{24}$. So the correct option is the fourth one, $\frac{18}{24}$.

Step2: Verify the ratio

Check the trigonometric ratio for angle A. $\cot A = \frac{\text{adjacent side to } A}{\text{opposite side to } A} = \frac{18}{24}$. So this matches the fourth option.

Answer:

$\frac{18}{24}$ (the fourth option, which is $\frac{18}{24}$)