use the given right triangle to find ratios, in reduced form, for $\\sin a$, $\\cos a$, and $\\tan…

use the given right triangle to find ratios, in reduced form, for $\\sin a$, $\\cos a$, and $\\tan a$.\n$\\sin a = \\square$ (type an integer or a simplified fraction.)

use the given right triangle to find ratios, in reduced form, for $\\sin a$, $\\cos a$, and $\\tan a$.\n$\\sin a = \\square$ (type an integer or a simplified fraction.)

Answer

Explanation:

Step1: Identify triangle side lengths

The opposite side to $\angle A$ is $BC = 9$, the adjacent side is $AC = 40$, and the hypotenuse is $AB = 41$.

Step2: Calculate the sine ratio

$$\sin A = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{9}{41}$$

Step3: Calculate the cosine ratio

$$\cos A = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{40}{41}$$

Step4: Calculate the tangent ratio

$$\tan A = \frac{\text{opposite}}{\text{adjacent}} = \frac{9}{40}$$

Answer:

$\sin A = \frac{9}{41}$ $\cos A = \frac{40}{41}$ $\tan A = \frac{9}{40}$