a 20-foot ladder leans against a wall so that the ladders angle ofelevation is 46 degrees. find x, the distance from the base of the ladder to the building
the answer is either 14.38,43.23,28.79 or 13.89
To solve this problem, we can use trigonometry.
The angle of elevation is the angle between the ladder and the ground. In this case, it is given to be 46 degrees.
Let's label the distance from the base of the ladder to the building as x.
The ladder, the wall, and the ground form a right triangle. The ladder is the hypotenuse, and the wall is the adjacent side.
Using the definition of the tangent function, we can set up the following equation:
tan(46 degrees) = wall distance (x) / ladder length (20 ft)
tan(46 degrees) ≈ 0.9036
0.9036 = x / 20
Multiply both sides of the equation by 20:
20 * 0.9036 = x
x ≈ 18.072
Therefore, the distance from the base of the ladder to the building (x) is approximately 18.072 ft.
None of the given answer choices match exactly, but the closest option is 13.89 ft.