A right-angled triangle has one angle of 60 degrees, the hypotenuse and the smaller leg are 18 cm.

A right-angled triangle has one angle of 60 degrees, the hypotenuse and the smaller leg are 18 cm. Find the hypotenuse and the smaller leg.

According to the condition of the problem, one of the acute angles is 60 °, which means that the second acute angle of a right-angled triangle is:
90 ° – 60 ° = 30 °.
The smaller leg is located opposite an angle of 30 °, respectively, equal to half the hypotenuse.
Let us introduce the proportionality coefficient k:
k cm – smaller leg;
2k cm – hypotenuse.
Together, their lengths are 18 cm.We get the equation:
k + 2k = 18
3k = 18
k = 6 (cm) – smaller leg;
2 * 6 = 12 (cm) – hypotenuse.
Answer: 6 cm and 12 cm of the length of the smaller leg and hypotenuse, respectively.