Question

12/20 which triangle below shows the ratio as \\( \cos ( x ) = \frac { u } { v } \\)?

Explanation:

Step1: Recall the cosine formula

For a right - triangle, \(\cos(x)=\frac{\text{adjacent}}{\text{hypotenuse}}\).

Step2: Analyze the first triangle

In the first triangle, the adjacent side to angle \(x\) is \(u\) and the hypotenuse is \(y\). So \(\cos(x)=\frac{u}{y}\).

Step3: Analyze the second triangle

In the second triangle, the adjacent side to angle \(x\) is \(u\) and the hypotenuse is \(l\). So \(\cos(x)=\frac{u}{l}\).

Step4: Analyze the third triangle

In the third triangle, the adjacent side to angle \(x\) is \(v\) and the hypotenuse is \(u\). So \(\cos(x)=\frac{v}{u}\).

Since the problem asks for \(\cos(x)=\frac{u}{v}\), none of the given triangles satisfy the ratio \(\cos(x)=\frac{u}{v}\).

Answer:

No triangle among the given options shows the ratio \(\cos(x)=\frac{u}{v}\).