In triangle ABC, angle C is 90 °, cosA = 1 / √5. Find the tangent of the outer angle at the vertex A.

In this problem, we first need to recall the basic trigonometric identity, which looks like this: sin²A + cos²A = 1. In the problem there is a value of the cosine of angle A, which means that we can find the sine of angle A. Below is a link to a detailed finding of the sine of angle A.

Further, we will use the fact that the tangent of an angle is equal to the ratio of the sine of this angle to its cosine. Substitute the obtained and already known numerical data and calculate the result. We got the value of the tangent of angle A.

The tangent of the outer angle at the vertex A is equal to the tangent of the angle A, but with the opposite sign. That is, the tangent of the outer corner is – 2.

Answer: – 2.