13) Given a right-angled triangle with one leg 7 cm and the hypotenuse 14 cm. Find the angle α.

Solution:

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

\( \sin(\alpha) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{7 \text{ cm}}{14 \text{ cm}} = 0.5 \)

Now, we find the angle whose sine is 0.5:

\( \alpha = \arcsin(0.5) = 30^{\circ} \)

Answer: \(\alpha = 30^{\circ}\)