In the trapezoid, one of the lateral sides is perpendicular to the bases and is equal to 8 dm.

In the trapezoid, one of the lateral sides is perpendicular to the bases and is equal to 8 dm. The smaller diagonal is perpendicular to the side and forms an angle with the smaller base, the tangent of which is 4/3. Find another side and base.

In a right-angled triangle ABC tgACB = 4/3 = AB / BC.

BC = AB * 3/4 = 8 * 3/4 = 6 dm.

Then AC ^ 2 = BC ^ 2 * AB ^ 2 = 36 + 64 = 100.

AC = 10 dm.

The angle CAD is equal to the angle ACB as the intersecting angles are parallel to BC and AD of the secant AC, then tgACB = tgCAD = 4/3.

Then tgCAD = 4/3 = CD / AC = CD / 10.

CD = 10 * 4/3 = 40/3 = 13 (1/3) dm.

AD ^ 2 = AC ^ 2 + CD ^ 2 = 100 + (1600/9) = 2500/9.

AD = 50/3 = 16 (2/3) dm.