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Every triangle has six measurements which are also known as six elements of a triangle. They are three sides and three angles.

Note that lower case letters such as a, b, c.... are used to denote the length of sides (or to name the sides) of a triangle that are opposite the anlges named with corresponding upper-case letters Ð A, Ð B, Ð C ..... resp.

Generally when any three elements are given, the remaining three elements can be found out (except the case when only the three angles are given; for in this case we do not get the definite values of sides).

Solution of a triangle : The process of finding out the other elements of a triangle when any three elements are given (except the case of three angles) is called the solution of the triangle.

3.1 Solving Right Triangles

Cases : When given
(I) Hypotenuse and one side.
(II) Two sides other than hypotenuse.
(III) One angle (other than right angle) and its opposite side.
(IV) One angle (other than right angle) and its adjacent side (other than hypotenuse).
(V) One angle (other than right angle) and hypotenuse.

Clearly speaking still many cases exist. But for a right triangle all these are easy !

(I) Hypotenuse and one side : Let 'b' and hypotenuse 'c' be given. Solving the right triangle as a2 = c2 - b2 . Hence 'a' is known. Consider sin B = b / c using calculator or table Ð B can be known. Also Ð A = 90 - m Ð B \ Ð A is known.

Now here all the sides and angles are known, hence the triangle is solved.

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3. 1 Solving Right Triangles
3. 2 Law of Cosines
3. 3 Law of Sines
3. 4 The Ambiguous Case of Law of Sines
3. 5 Areas of Triangles
Supplementary Problems

Chapter 4

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