skylar leans a 24 - foot ladder against a wall so that it forms an angle of 60° with the ground. whats the…

skylar leans a 24 - foot ladder against a wall so that it forms an angle of 60° with the ground. whats the horizontal distance between the base of the ladder and the bottom of the wall? round your answer to the nearest hundredth of a foot if necessary.

skylar leans a 24 - foot ladder against a wall so that it forms an angle of 60° with the ground. whats the horizontal distance between the base of the ladder and the bottom of the wall? round your answer to the nearest hundredth of a foot if necessary.

Answer

Explanation:

Step1: Aplicar la función trigonométrica coseno

La relación entre el cateto adyacente ((x), la distancia horizontal), la hipotenusa ((24) pies) y el ángulo de (60^{\circ}) se da por (\cos\theta=\frac{\text{cateto adyacente}}{\text{hipotenusa}}). Entonces (\cos(60^{\circ})=\frac{x}{24}).

Step2: Resolver para (x)

Sabemos que (\cos(60^{\circ}) = 0.5). Sustituyendo en la ecuación (0.5=\frac{x}{24}), multiplicando ambos lados por (24) obtenemos (x = 24\times0.5).

Answer:

(12.00) pies