Question

1. solve for x using the tangent function.

right triangle with right angle at top left, horizontal leg length 9, vertical leg labeled x, angle at bottom left is 45 degrees
options: 9, 12.73, 6.36, 11.58

Explanation:

Step1: Recall Tangent Definition

In a right triangle, \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 45^\circ\), opposite side to \(45^\circ\) is \(9\), adjacent is \(x\). So \(\tan(45^\circ)=\frac{9}{x}\).

Step2: Solve for \(x\)

We know \(\tan(45^\circ) = 1\). So \(1=\frac{9}{x}\), which gives \(x = 9\) (by cross - multiplying: \(x\times1=9\times1\)).

Answer:

9 (corresponding to the first option, e.g., A. 9 if options are labeled A, B, C, D with A being 9)