Final answer:
The tangent of the other complementary angle in a right triangle can be found by taking the reciprocal of the given tangent since the product of the tangents of complementary angles is 1.
Step-by-step explanation:
If we are given the tangent of one of the complementary angles in a right triangle ABC, where ∠C = 90 degrees, we can find the tangent of the other angle using the fact that the sum of the angles in a triangle is 180 degrees, and because the angles are complementary in a right triangle, their sum is 90 degrees.
The tangent function is the ratio of the opposite side over the adjacent side in a right triangle. If we know tan A for one angle, we can find tan B for the complementary angle by using the identity tan B = 1 / tan A, since tan(A) * tan(B) = 1 for two acute complementary angles in a right triangle.
To illustrate, if tan A = Ay/Ax, then tan B would be Ax/Ay. In other words, for complementary angles A and B, the tangent of angle A is the reciprocal of the tangent of angle B.