SAT Mathematics Practice Test 6

In right triangle ABC, the measure of angle B must be $58^{\circ}$ because the sum of the measure of angle A, which is $32^{\circ}$, and the measure of angle B is $90^{\circ}$. Angle D in the right triangle DEF has measure $58^{\circ}$. Hence, triangles ABC and DEF are similar. Since BC is the side opposite to the angle with measure 32° and AB is the hypotenuse in right triangle ABC, the ratio $\frac{BC}{AB}$ is equal to $\frac{DF}{DE}$ Alternate approach: The trigonometric ratios can be used to answer this question. In right triangle ABC, the ratio $\frac{BC}{AB} = \sin(32^{\circ})$ The angle E in triangle DEF has measure 32° because m(∠D)+m(∠E)=90° In triangle DEF, the ratio $\frac{DF}{DE} = \sin(32^{\circ})$.Therefore,$\frac{DF}{DE} = \frac{BC}{AB}$ Choice A is incorrect because $\frac{DE}{DF}$ is the inverse of the ratio $\frac{BC}{AB}$.Choice C is incorrect because $\frac{DF}{EF} = \frac{BC}{AC}$, not $\frac{BC}{AB}$.Choice D is incorrect because $\frac{EF}{DE} = \frac{AC}{AB}$,not $\frac{BC}{AB}$