TRIGONOMETRY II

The angles of a triangle

The sum of the three angles of a triangle

With the Descartes applet below, any triangle can be drawn. Even though A is a fixed point and B is moves only horizontally, any triangular form can be obtained.   The line that passes through C is parallel to the side AB and is planned to show why the three angles of any triangle add up to 180º.

Draw the triangles in which the following conditions are fulfilled:
a) A=90º, AB=4 y AC=3 b) B=90º, AB=4, A=45º c) AB=3, B=120º, A=30º.

The area of a triangle

The Descartes applet below allows us to investigate the area of any triangle.

Draw a right-angled triangle (A=90º) with base AB=4 and height 3. Calculate its area.  Can you explain why it is obtained multiplying the base by the height and dividing by two? Which will the area of the triangles with the same base and height be, that is to say, those obtained moving the vertex C horizontally?

Solution of triangles

Solving a triangle means to find the value of all its sides and angles when some of them are known.  The Initial triangle of the Descartes applet below is determined by the position of its three vertices A(0,0), B(3,0) and C(4,3); from them the lengths of the sides, and the angles are known. 

Draw a triangle which has the side AB=4, the side AC=5 and the included angle between the two A=60º. Draw a triangle of which it is known that the side AB=5 and the angles A=30º and B=120º. Can a triangle with sides AC=6, CB=5 and angle A=45 be drawn?   Could there be more than one triangle that fulfils this condition?

Author: Miguel García Reyes

	Ministerio de Educación, Cultura y Deporte. Año 2000