After take-off, planes ascend at an angle to reach their cruising altitude. This angle of elevation is related to the opposite and adjacent sides of a right triangle through the tangent ratio, which is the opposite side divided by the adjacent side. For any right triangle with the same angle, the tangent ratio of opposite over adjacent will be the same value. Solving tangent triangle problems involves labeling sides, determining what is unknown (opposite, adjacent, or angle), and using the appropriate tangent formula along with a calculator set to degrees mode.