Two friends are writing practice problems to study for a trigonometry test. Sam writes the following problem for his friend Anna to solve: In right triangle ABC, the measure of angle C is 90 degrees, and the length of side c is 8 inches.
Solve the triangle.
Anna tells Sam that the triangle cannot be solved. Sam says that she is wrong.
Who is right? Explain your thinking

Anna is right in her meaning concerning on triangle solvability.

Step-by-step explanation:

The side represents the hypotenuse of a right triangle as and is opposite to that angle. There are two ways to solve this triangle trigonometrically:

i) Law of Sine

(1)

ii) Law of Cosine

(2)

The Pythagorean Theorem is a particular case of the Law of Cosine for

The triangle cannot be solved as there is an input missing, either another side or another angle. If , then (2) is reduced into this form:

(2b)

In this case we need to know the measure of either or to determine its counterpart and the values of the missing angles by (1). In nutshell, Anna is right.