Question

1. solve for x using the tangent function.

29
65°
x
13.5
11.4
62.2
35.8

Explanation:

Step1: Recall Tangent Definition

In a right triangle, $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 65^\circ$, opposite side is $29$, adjacent is $x$. So $\tan(65^\circ) = \frac{29}{x}$.

Step2: Solve for x

Rearrange: $x = \frac{29}{\tan(65^\circ)}$. Calculate $\tan(65^\circ) \approx 2.1445$. Then $x \approx \frac{29}{2.1445} \approx 13.5$. Wait, no—wait, maybe I mixed opposite and adjacent. Wait, the angle is $65^\circ$, the side adjacent to $65^\circ$ is $x$, opposite is $29$? Wait no, the right angle is at the bottom right, so the angle at bottom left is $65^\circ$, so the side opposite $65^\circ$ is the vertical side (29), and adjacent is $x$ (horizontal). So $\tan(65^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{29}{x}$. So $x = \frac{29}{\tan(65^\circ)}$. Wait, $\tan(65) \approx 2.1445$, so $29 / 2.1445 \approx 13.5$. Wait, but let's check again. Wait, maybe I had it reversed. Wait, if the angle is $65^\circ$, and the vertical side is 29, horizontal is x. So $\tan(65) = 29 / x$ → $x = 29 / \tan(65) ≈ 29 / 2.1445 ≈ 13.5$. So the first option is 13.5.

Answer:

13.5 (the option with 13.5)