In a right triangle, one acute angle measures 35°, and the leg adjacent to that angle has length 10. Which value is closest to the length…

The opposite and adjacent legs are connected by the tangent: $\tan 35^\circ=\frac{\text{opposite}}{10}$, so the opposite leg is $10\tan35^\circ\approx10(0.700)=7.0$, choice J. Choice G ($12.2$) is $\frac{10}{\cos35^\circ}$, the hypotenuse, not a leg. Choice F ($5.7$) is $10\sin35^\circ$, which would be correct only if 10 were the hypotenuse. Choice H ($8.2$) is $10\cos35^\circ$, another ratio that uses the wrong side. Match the ratio to the sides given: opposite over adjacent is the tangent.