Question

a right - triangle has side lengths 8, 15, and 17 as shown below. use these lengths to find sin m, tan m, and cos m.
cos m=

tan m=

sin m=

Explanation:

Step1: Recall trigonometric - ratio definitions

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\tan\theta = \frac{\text{opposite}}{\text{adjacent}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$ for an acute angle $\theta$. For angle $M$, the opposite side has length $15$, the adjacent side has length $8$, and the hypotenuse has length $17$.

Step2: Calculate $\sin M$

$\sin M=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{15}{17}$

Step3: Calculate $\tan M$

$\tan M=\frac{\text{opposite}}{\text{adjacent}}=\frac{15}{8}$

Step4: Calculate $\cos M$

$\cos M=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{8}{17}$

Answer:

$\sin M=\frac{15}{17}$, $\tan M=\frac{15}{8}$, $\cos M=\frac{8}{17}$