a 16-foot ladder leans against a wall so that the ladder's angle of elevation is 55 degree. 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 can use cosine to solve for the missing side.
The cosine of an angle is equal to the adjacent side divided by the hypotenuse.
In this case, the adjacent side is x and the hypotenuse is the length of the ladder, which is 16ft.
So we have the equation:
cos(55°) = x/16
To solve for x, we can rearrange the equation:
x = 16 * cos(55°)
Using a calculator to find the cosine of 55°, we get:
x ≈ 16 * 0.5736
Evaluating this expression, we get:
x ≈ 9.1776
Rounding to the nearest hundredth, 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.