Home » C Program For Law Of Sine Problems

# C Program For Law Of Sine Problems

With the law of sine, you can find any unknown angle of a given triangle or the length of a particular side of a triangle or the length of a particular side of a triangle. This is a fundamental concept of trigonometry.

We used Dev-C++ to compile the program, but you may use any other standard C compiler. This program make use of math header – math.h  especially, two trig functions – sin () function and asin () function at lot. So if you are choosing a different compiler then use the correct math header file.

Before you try the example, learn following C programming concepts. You can skip it if already know it well.

### Problem Definition

The law of sine is given below. The triangle has three sides $a, \hspace{1ex} b,$ and $c$; It also has three angles – $\angle A, \hspace{1ex} \angle B$ and $\angle C$.

In general, there are two cases for problems involving the law of sine.

#### Case 1: When the length of two sides are given and the angle opposite to one of the sides with length is given.

When the length of two side – $A$ and $B$ are given and the angle opposite to side $\hspace{1ex} A$ is given. Then using law of sine

$X \hspace{1ex} = \hspace{1ex} sin \hspace{1ex} A/a$
$sin \hspace{1ex} B/b \hspace{1ex} = \hspace{1ex} X$
$sin \hspace{1ex} B \hspace{1ex} =\hspace{1ex} X \hspace{1ex}\ast \hspace{1ex}b$
$Angle \hspace{1ex} B \hspace{1ex} = \hspace{1ex} arcsin ( X \ast b)$

This the way to find the value of sin $B$ and then using arcsin to find the $\angle B$.