Question

analyzing student work
kevin was asked to determine the length of side xz. his work is shown.
which error did kevin make?
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.

1. cos(34°) = 18/xz
2. (xz)cos(34°) = 18
3. xz = 18/cos(34°) ≈ 21.7

Explanation:

Step1: Recall cosine ratio definition

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. In right - triangle $XZY$ with right - angle at $Z$, if $\theta = 34^{\circ}$, the adjacent side to the $34^{\circ}$ angle is $XZ$ and the hypotenuse is $XY = 18$. So the correct cosine ratio should be $\cos(34^{\circ})=\frac{XZ}{18}$, not $\cos(34^{\circ})=\frac{18}{XZ}$.

Answer:

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