Lösung 4.2:8

Aus Online Mathematik Brückenkurs 1

Wechseln zu: Navigation, Suche

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

Vorlage:Displayed math

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

Vorlage:Displayed math

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

Vorlage:Displayed math

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

Vorlage:Displayed math

where \displaystyle \gamma is the only unknown.