Plane trigonometry, by S.L. Loney.

CHAPTER XIII.

SOLUTION OF TRIANGLES.
174. IN any triangle the 3 sides and the 3 angles are
often called the elements of the triangle. When any 3
elements of the triangle are given, provided they be not the
3 angles, the triangle is in general completely known, i.e.
its other angles and sides can be calculated. When the 3
angles are given, only the ratios of the lengths of the sides
can be found, so that the triangle is given in shape only
and not in size. When 3 elements of a triangle are given
the process of calculating its other 3 elements is called
the Solution of the Triangle.
We shall first discuss the solution of right-angled
triangles, i.e. triangles which have one angle given equal
to a right angle.
The next four articles refer to such triangles, and C
denotes the right angle.
175. Case I. Given the hypothenuse and one side, to
solve the triangle.