Question

three ballet dancers are positioned on stage. cameron is straight behind ken and directly left of natalie. if ken and cameron are 7.4 feet apart, and natalie and ken are 9.7 feet apart, what is the distance between cameron and natalie? if necessary, round to the nearest tenth. feet

Explanation:

Step1: Aplicar el Teorema de Pitágoras

Sea \(a = 7.4\) (distancia entre Ken y Cameron), \(c=9.7\) (distancia entre Natalie y Ken). Buscamos \(b\) (distancia entre Cameron y Natalie).
Según el Teorema de Pitágoras \(a^{2}+b^{2}=c^{2}\), entonces \(b^{2}=c^{2}-a^{2}\).
Sustituimos valores: \(b^{2}=9.7^{2}-7.4^{2}\).
Calculamos \(9.7^{2}=94.09\) y \(7.4^{2}=54.76\).
Luego \(b^{2}=94.09 - 54.76=39.33\).

Step2: Calcular \(b\)

Tomamos la raíz cuadrada de \(b^{2}\), \(b=\sqrt{39.33}\approx6.3\).

Answer:

\(6.3\)