Question

which triangle below shows the ratio as \\( \tan ( x ) = \frac { t } { u } \\)?

Explanation:

Step1: Recall the tangent formula

In a right - triangle, \(\tan(x)=\frac{\text{opposite}}{\text{adjacent}}\)

Step2: Analyze each triangle

• For the first triangle: \(\tan(x)=\frac{t}{u}\) (opposite side is \(t\), adjacent side is \(u\))
• For the second triangle: \(\tan(x)=\frac{v}{u}\) (opposite side is \(v\), adjacent side is \(u\))
• For the third triangle: \(\tan(x)=\frac{t}{v}\) (opposite side is \(t\), adjacent side is \(v\))

Answer:

The first triangle.