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.
Let x be the distance between the foot of the ladder and the base of the building.
Using cosine, we have: cos(55°) = x / 16.
Multiplying both sides by 16, we get: x = 16 * cos(55°).
Evaluating cos(55°), we find: x = 16 * 0.5736.
Simplifying, we have: x ≈ 9.18.
Therefore, the distance between the foot of the ladder and the base of the building is approximately 9.18 feet.