Question

solving for side lengths of right triangles
analyzing student work
kevins work

1. cos(34) = (\frac{xz}{18})
2. (xz)cos(34) = 18
3. xz=(\frac{18}{cos(34)}approx21.7)

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 trigonometric ratios

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Given the angle $34^{\circ}$ and the side length $16$ which is opposite to the angle $\angle X$. To find the side $XZ$ (adjacent to the angle $\angle X$), we should use the tangent ratio $\tan(34^{\circ})=\frac{16}{XZ}$. Kevin used the cosine ratio incorrectly.

Answer:

He should have used the tangent ratio.