Ejemplo 3. Construcción de un triángulo conocido un lado y los dos ángulos adyacentes

[i]Construye el triángulo en el que un lado mide 5,34 y los ángulos adyacentes son 40[/i][i]⁰[/i][i] y 83[/i][i]⁰[/i][i].[/i][br][br]Comenzamos igual que en los dos ejemplos anteriores, utilizando la herramienta [b]Circunferencia (centro-radio)[/b] para trasladar la medida del lado conocido. Una vez dibujada la circunferencia, cualquier punto de ella determinará la medida de dicho lado.[br][br][img width=356,height=198]data:image/png;base64,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continuación, debemos trasladar la medida de los dos ángulos, para lo que utilizaremos la herramienta[br][b]Ángulo dada su amplitud[/b], de manera similar al ejemplo anterior.[br]Comenzamos por el primero de los ángulos cuya medida es de 40⁰, por lo que una vez seleccionada la herramienta, marcamos B, A e introducimos dicho valor, para obtener un nuevo punto B’ que uniremos con A con una semirrecta.[br][br][img 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continuación, repetimos el proceso para la medida del segundo ángulo que trasladamos al vértice B, por lo que seleccionamos de nuevo la herramienta Ángulo dada su amplitud, marcando A, B e introduciendo la medida de 83⁰; estableciendo el sentido horario para crear el ángulo.[br][br][img 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[/img][br][br]Obtenemos un nuevo punto A’ que uniremos con una semirrecta con B.[br][br][img 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establecido el sentido contrario para que los dos puntos A’ y B’ queden por encima del segmento AB.[br]El tercer vértice del triángulo será el punto de intersección de las dos semirrectas que obtenemos con la herramienta [b]Intersección[/b].[br]Una vez obtenido el punto C sólo queda dibujar el triángulo que tiene las medidas dadas.[br][br][img 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Information: Ejemplo 3. Construcción de un triángulo conocido un lado y los dos ángulos adyacentes