Answer:
A
Explanation:
Let's label what we currently have:
![Hypotenuse = x](https://img.qammunity.org/2020/formulas/mathematics/middle-school/bigqx1s79gs2ibu66ihf8h0577eutk947p.png)
![Opposite = 12](https://img.qammunity.org/2020/formulas/mathematics/middle-school/c4wu6yodaiagytgo9exb2c3nynyob714ij.png)
![Adjacent = ?](https://img.qammunity.org/2020/formulas/mathematics/middle-school/8dtf1amewe44m4udk0sr9ufenpi9dnb510.png)
Since the answer choices are asking us to use cosine, we will need to use the cosine formula:
![cos=(adjacent)/(hypotenuse)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/z97ekt22n7g5uivbb1p5k6ymi7tl2m5coi.png)
It seems like we don't have the adjacent side yet. However, if we use another angle, we can find out what x is. We know one angle is 35°. Since it is a right triangle, the other angle is 90°. Since all triangles add up to 180°, we know that the other angle is 55°. We CAN use cosine to find x if we use the 55° angle.
Let's label our new areas:
![Hypotenuse=x](https://img.qammunity.org/2020/formulas/mathematics/middle-school/qqb8sw80tgrsdn892si7c28zznxmajiwt0.png)
![Opposite=?](https://img.qammunity.org/2020/formulas/mathematics/middle-school/jag8hjo92vhjq4fyy3l7qmot6f2yuj3ud1.png)
![Adjacent=12](https://img.qammunity.org/2020/formulas/mathematics/middle-school/qpia1y69ddsrjoyptyf3nlv7rvq7t9clnw.png)
By using the cosine formula, we can now use the two values we have in the equation.
![cos 55=(12)/(x)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/eqzjf45p4xrw36gvsctt8pnmyxv2ikkwk5.png)