From the angles of a right-angled triangle 30 degrees and the sum of the hypotenuse

From the angles of a right-angled triangle 30 degrees and the sum of the hypotenuse and the opposite leg is 21 cm, the perimeter of 33.12 cm is to find its legs.

1) Knowing that the sum of the hypotenuse and one of the legs is 21, and the perimeter of the triangle is 33.12 cm, we can find the third leg. To do this, subtract a known amount from the perimeter:

33.12 – 21 = 12.12 – the length of the third leg.

2) There is a property according to which opposite an angle of 30 degrees lies a leg equal to half of the hypotenuse.

Therefore, the sum of the hypotenuse and this leg is 3/2 of the hypotenuse:

21/3 = 7 – the length of the second leg;

21 – 7 = 14 is the length of the hypotenuse.