The base of the trapezoid is 27 and 9, the side is 8. The area of the trapezoid is 72.

The base of the trapezoid is 27 and 9, the side is 8. The area of the trapezoid is 72. Find the acute angle of the trapezoid adjacent to the given side.

1. The lower base of the trapezoid is: A = 27 cm;

2. Upper base of the trapezoid: B = 9 cm;

3. The lateral side is equal to: C = 8 cm;

4. Area of the trapezoid: St = 72 cm²;

St = ((A + B) / 2) * H;

5. We calculate the height of the trapezoid: Ht cm;

Ht = (2 * St) / (A + B) = 2 * 72 / (27 + 9) = 144/36 = 4 cm;

6. For a laterally-adjacent acute angle (a), the aspect ratio is:

Ht / C = sina = 4/8 = 1/2;

7. Determine the angle a:

a = arcsin (1/2) = 30 °.

Answer: The angle between the bottom base and the side is 30 °.