Relații metrice

1. The given image shows the right triangle ABC and the height corresponding to the side BC. Knowing that BC is 12 cm and CD is 3 times smaller than BC, find the length of AD (the height). (write the number and unit of measurement)

2. Using the same triangle with the same measurements, determine the lengths of the catheti of the triangle ABC.

3. Deducing from the given drawing, the sides of the right triangle ABC, AB, BC & AC have the following values - 1, √3 & 2. Find the sin, cos, tan & cotan of the α angle. (choose 4 correct options for each unknown unit)

4. For a math competition, the event managers need to arrange square tables so that they get a right triangle every 3 tables (as in the image). Knowing that the perimeter of the edges of TABLE 1 is 4.80 m and the perimeter of TABLE 2 is 6.4 m, find the area of ​​the third table (the largest). (just write the number)