Question

a 16-foot ladder leans against a wall so that the ladders angle of elevation is 55°. find x, the distance between the foot of the ladder and the base of the building. use cosine to solve for the missing side and round your answer to the nearest hundredth. (1 point) \\(\bigcirc\\) x = 13.11 \\(\bigcirc\\) x = 27.90 \\(\bigcirc\\) x = 52.87 \\(\bigcirc\\) x = 9.18

Explanation:

Step1: Define cosine relationship

$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

Step2: Substitute known values

$\cos(55^\circ) = \frac{x}{16}$

Step3: Solve for x

$x = 16 \times \cos(55^\circ)$

Step4: Calculate and round

$x \approx 16 \times 0.5736 = 9.1776 \approx 9.18$

Answer:

x = 9.18