Find sin, cos, tg of the acute angle of a rectangular trapezoid, the smaller side of which is 5 cm

Find sin, cos, tg of the acute angle of a rectangular trapezoid, the smaller side of which is 5 cm, and the difference between the bases is 12 cm.

Obviously, the smaller side is the one that forms a right angle with the larger base.

Let us mentally draw the height from an obtuse angle to the larger base. We get a right-angled triangle, where one leg will be equal to the lower height, and the second will be equal to the difference in bases.

Let us determine what the lateral side will be equal to, which forms with a large base the acute angle we need:

√ (12 ^ 2 + 5 ^ 2) = √169 = 13.

Determine the cosine of the angle:

12: 13 = 12/13.

Determine the sine of the angle:

5: 13 = 5/13.

Determine the tangent of the angle:

5: 12 = 5/12.

Answer: cos = 12/13, sin = 5/13, tg = 5/12.