Question

a right triangle has side lengths 9, 40, and 41 as shown below. use these lengths to find cos x, tan x, and sin x.
cos x =
□
tan x =
□
sin x =
□

Explanation:

Step1: Recall trig - ratio definitions

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, and $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$ for an acute angle $\theta$. For angle $X$, the opposite side to $X$ is $9$, the adjacent side to $X$ is $40$, and the hypotenuse is $41$.

Step2: Calculate $\sin X$

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

Step3: Calculate $\tan X$

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

Step4: Calculate $\cos X$

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

Answer:

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