Question

Label the diagram for the reference angle. Write the formula first, then the ratio. Don't be fooled

Answer 1

ANSWER and EXPLANATION

We have the triangle given and we have to first label it for the missing angle.

The missing angle is 33 degrees and that is the measure of MNP.

Let us add it to the diagram:

Now, to find the correct ratio for each trigonometric value written, we apply trigonometric ratios SOHCAHTOA:

`\begin{gathered} \sin (\theta)\text{ = }(opposite)/(hypotenuse) \\ \cos (\theta)\text{ = }(adjacent)/(hypotenuse) \\ \text{where }\theta\text{ = angle considered} \end{gathered}`

Therefore, we have that:

`\begin{gathered} \sin 57\text{ = }(15)/(x) \\ \sin 33\text{ = }(7)/(x) \\ \cos 57\text{ = }(7)/(x) \\ \cos 33\text{ = }(15)/(x) \end{gathered}`

That is the correct ratio for each trigonometric value.