Question

Write the ratios for sin M, cos M, and tan M.

Answer 1

`\sin(M) = (7)/(25)`

`\cos(M) = (24)/(25)`

`\tan(M) = (7)/(24)`

Explanation:

We can use the acronym SOH-CAH-TOA to remember the trigonometric ratios.

Sine

Opposite

Hypotenuse

`\implies \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}`

-

Cosine

Adjacent

Hypotenuse

`\implies \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}`

-

Tangent

Opposite

Adjacent

`\implies \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}`

Applying these ratios to the given triangle for angle M:

`\boxed{\sin(M) = (7)/(25)}`

`\boxed{\cos(M) = (24)/(25)}`

`\boxed{\tan(M) = (7)/(24)}`