In an isosceles right triangle, one of the angles is 90 degrees (the right angle), and the other two angles are congruent and each measures 45 degrees.

To find the tangent of angle A (one of the congruent angles), we can use the definition of the tangent function:

tan(A) = Opposite / Adjacent

In this case:

• The opposite side to angle A is the side opposite to the 45-degree angle, which is the shorter leg of the right triangle.
• The adjacent side to angle A is the side adjacent to angle A, which is also the shorter leg of the right triangle.

Since both the opposite and adjacent sides are the same in an isosceles right triangle, you have:

tan(A) = Opposite / Adjacent = 1 / 1 = 1

So, the tangent of angle A is 1.