Question

a ladder leans against the side of a house. the top of the ladder is 8 ft from the ground. the bottom of the ladder is 7 ft from the side of the house. find the length of the ladder. if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Aplicar el Teorema de Pitágoras

El Teorema de Pitágoras establece que \(a^{2}+b^{2}=c^{2}\), donde \(a = 7\), \(b = 8\) y \(c\) es la longitud de la escalera.
$$7^{2}+8^{2}=c^{2}$$

Step2: Calcular los cuadrados

$$49 + 64=c^{2}$$
$$113=c^{2}$$

Step3: Extraer la raíz cuadrada

$$c=\sqrt{113}$$
$$c\approx10.6$$

Answer:

\(10.6\)