a 16-foot ladder leans against a wall so that the ladders angle of elevation is 55 degrees. 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.
We are given that the ladder leans against a wall and forms an angle of elevation of 55 degrees. We need to find the distance, x, between the foot of the ladder and the base of the building.
We can use cosine to solve for x. The cosine of an angle is equal to the adjacent side divided by the hypotenuse. In this case, x is the adjacent side and the hypotenuse is the length of the ladder, which is 16 feet.
So, cos(55) = x / 16
To solve for x, we can multiply both sides of the equation by 16:
16 * cos(55) = x
Using a calculator to find the cosine of 55 degrees, we get:
16 * 0.573 = x
x ≈ 9.168
Therefore, the distance between the foot of the ladder and the base of the building, rounded to the nearest hundredth, is approximately 9.17 feet.