Question

which triangle below shows the ratio as \\( \tan ( x ) = \frac { c } { a } \\)

Explanation:

Step1: Recall the tangent formula

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

Step2: Analyze each triangle

• In the first triangle: \(\tan(x)=\frac{b}{a}\) (opposite = \(b\), adjacent=\(a\))
• In the second triangle: \(\tan(x)=\frac{a}{b}\) (opposite = \(a\), adjacent=\(b\))
• In the third triangle: \(\tan(x)=\frac{c}{a}\) (opposite = \(c\), adjacent=\(a\))

Answer:

The third triangle.