Question

In ΔMNO, the measure of ∠O=90°, ON = 16, NM = 65, and MO = 63. What ratio represents the cotangent of ∠M?

Answer 1

We can represent this triangle as follows:

We have six trigonometric ratios that can be applied to a right triangle like the one above.

We have that the ratio cotangent is given by:

`\cot (\theta)=(adj)/(opp)`

That is, the ratio cotangent is the adjacent side to the angle to the opposite side of the angle. In this case, the reference angle is
`\cot (\theta)=(MO)/(ON)\Rightarrow cot(\theta)=(63)/(16)`

Therefore, the ratio is cot(theta) = 63/16.