12) Given a right-angled triangle with legs 4 m and 8 m. Find the angle α.

Solution:

In a right-angled triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side.

\( \tan(\alpha) = \frac{\text{opposite}}{\text{adjacent}} = \frac{4 \text{ m}}{8 \text{ m}} = 0.5 \)

Now, we find the angle whose tangent is 0.5:

\( \alpha = \arctan(0.5) \approx 26.57^{\circ} \)

Answer: \(\alpha \approx 26.57^{\circ}\)