1. By the condition of the problem, it is known that in a right-angled triangle ABC the hypotenuse is 1 cm, the angle a = 30 °.
Let’s designate the legs as a and b.
2. To determine the legs, we will use trigonometric functions:
a) the sine of the angle is the ratio of the opposite leg to the hypotenuse;
b) the cosine of the angle is equal to the ratio of the adjacent leg to the hypotenuse.
a: 1 cm = sin 30 °, so a = 1 cm * sin 30 ° = 1 cm * 1/2 = 0.5 cm.
in: 1 cm = cos 30 °,
whence b = 1 cm * cos 30 ° = 1 cm * √3 / 2 = 1 cm * 1.7 / 2 = 0.85 cm.
Answer: The legs are 0.5 cm and 0.85 cm.
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