Question

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

In a right - triangle, $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$. In right - triangle $XZY$ with right - angle at $Z$, if $\theta = 34^{\circ}$, and the side adjacent to the $34^{\circ}$ angle is $YZ = 18$ and the hypotenuse is $XZ$. So, $\cos(34^{\circ})=\frac{YZ}{XZ}=\frac{18}{XZ}$.

Step2: Analyze Kevin's work

Kevin wrote $\cos(34^{\circ})=\frac{XZ}{18}$. He has the side lengths in the wrong place in the cosine ratio. The correct ratio should have the adjacent side ($YZ = 18$) in the numerator and the hypotenuse ($XZ$) in the denominator.

Answer:

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