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)
Let's denote x as the distance between the foot of the ladder and the base of the building.
We are given that the ladder's angle of elevation is 55°.
Using cosine, we can relate the adjacent side (x) to the hypotenuse (16 feet) using the formula:
cos(55°) = x / 16
To solve for x, we can multiply both sides by 16:
16 * cos(55°) = x
Using a calculator, we can determine that cos(55°) is approximately 0.5736.
To find x, we can substitute this value into the equation:
x = 16 * 0.5736
x ≈ 9.18
Therefore, the distance between the foot of the ladder and the base of the building (x) is approximately 9.18 feet.