A 16-foot ladder leans against a wall so that the ladder’s 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)
x=13.11 ft.
x=9.18 ft
x=52.87 ft.
x=27.90 ft.
To find x, the distance between the foot of the ladder and the base of the building, we can use cosine to solve for the missing side.
The cosine of an angle is defined as the adjacent side divided by the hypotenuse. In this case, the adjacent side is x and the hypotenuse is 16 feet.
So we can use the cosine function to solve for x:
cos(55°) = x/16
To isolate x, we can multiply both sides of the equation by 16:
16 * cos(55°) = x
Using a calculator, we find that cos(55°) is approximately 0.5736.
Thus,
16 * 0.5736 = x
x = 9.18 ft
Therefore, the distance between the foot of the ladder and the base of the building is approximately 9.18 ft.
So the correct answer is x = 9.18 ft.