Question

kevin was asked to determine the length of side xz. his work is shown. 1. cos(34°) = 18 / xz 2. (xz)cos(34°) = 18 3. xz = 18 / cos(34°) ≈ 21.7 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.

Explanation:

Step1: Recall cosine - ratio formula

In right - triangle $\triangle XYZ$ with right - angle at $Z$, $\cos(X)=\frac{adjacent}{hypotenuse}$. Here, $\cos(34^{\circ})=\frac{YZ}{XZ}$, not $\frac{XZ}{YZ}$. Kevin has the side lengths in the wrong place in the cosine ratio.

Answer:

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