Question

kevin was asked to determine the length of side xz. his work is shown. which error did kevin make? 1. $\cos(34^{\circ}) = \frac{18}{xz}$ 2. $(xz)\cos(34^{\circ}) = 18$ 3. $xz = \frac{18}{\cos(34^{\circ})} \approx 21.7$ options: he has the side lengths in the wrong place in the cosine ratio. he multiplied both sides by the length of xz instead of dividing by xz. he should have used the sine ratio. he should have used the tangent ratio.

Explanation:

In right triangle $XZY$, for $\angle X = 34^\circ$, the adjacent side to the angle is $XZ$, the hypotenuse is $XY = 18$. The correct cosine ratio is $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$, so $\cos(34^\circ)=\frac{XZ}{18}$. Kevin incorrectly placed the sides as $\cos(34^\circ)=\frac{18}{XZ}$, swapping the adjacent side and hypotenuse in the cosine ratio.

Answer:

He has the side lengths in the wrong place in the cosine ratio.