Question

5.
angle (θ)
opposite
adjacent
hypotenuse
trig function

Explanation:

Step1: Identify sides and angle

In right triangle \( \triangle ABC \) with \( \angle C = 90^\circ \), \( \angle A = 41^\circ \), opposite side to \( \angle A \) is \( BC = 4 \), adjacent side is \( AC = x \), hypotenuse is \( AB \). We use tangent function: \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \). So \( \tan(41^\circ) = \frac{4}{x} \).

Step2: Solve for \( x \)

Rearrange the formula: \( x = \frac{4}{\tan(41^\circ)} \). Calculate \( \tan(41^\circ) \approx 0.8693 \), then \( x \approx \frac{4}{0.8693} \approx 4.60 \).

Answer:

\( x \approx 4.60 \)