Question

find tan (a) given the triangle. enter your answer as a fraction or as a decimal rounded to three decimal places. draw

Explanation:

Step1: Recall tangent definition

In a right triangle, $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ to angle $\theta$.

Step2: Identify sides for angle \(a\)

Opposite side to \(a\) is \(48\), adjacent side is \(140\).

Step3: Calculate \(\tan(a)\)

$\tan(a) = \frac{48}{140}$
Simplify: $\frac{48}{140} = \frac{12}{35} \approx 0.342857$
Round to three decimal places: \(0.343\)

Answer:

\(0.343\) (or \(\frac{12}{35}\))