Solution 4.2:8

From Förberedande kurs i matematik 1

We start by drawing three auxiliary triangles, and calling the three vertical sides x y and z, as shown in the figure.

Using the definition of cosine, we can work out x and y from

x=acos

y=bcos

and, for the same reason, we know that z satisfies the relation

z=lcos

In addition, we know that the lengths x y and z satisfy the equality

z=x−y

If we substitute in the expressions for x y and z, we obtain the trigonometric equation

lcos=acos−bcos

where is the only unknown.