Exercise 26 Page 656

Let's begin with drawing a 45^(∘)-45^(∘)-90^(∘) triangle. If we call the legs of this right isosceles triangle x, then the hypotenuse is xsqrt(2).

In our exercise we are asked to evaluate the tangent of 45^(∘). Recall that the tangent of ∠ A is the ratio of the length of the leg opposite ∠ A to the length of the leg adjacent ∠ A. Using this definition, we can write the appropriate ratio for 45^(∘).

The tangent of 45^(∘) is 1.