Question

1. solve for x using the tangent function.

triangle image with 40° angle, x, 15, right angle
options: 11.49, 9.64, 17.87, 21.73

Explanation:

Step1: Recall Tangent Definition

In a right triangle, $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 40^\circ$, opposite side to $40^\circ$ is $15$, adjacent side is $x$. So $\tan(40^\circ) = \frac{15}{x}$.

Step2: Solve for x

Rearrange the formula: $x = \frac{15}{\tan(40^\circ)}$. Calculate $\tan(40^\circ) \approx 0.8391$. Then $x = \frac{15}{0.8391} \approx 17.87$.

Answer:

17.87