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
We can use the trigonometric function tangent to solve this problem.
The tangent of an angle is the ratio of the length of the opposite side (in this case, the distance from the base of the ladder to the building) to the length of the adjacent side (in this case, the height of the wall).
We know that the angle of elevation is 46 degrees and the height of the wall is 20 feet.
Using the tangent function: tan(angle) = opposite/adjacent
tan(46 degrees) = x/20 feet
We can solve for x by multiplying both sides by 20 feet and taking the tangent of 46 degrees.
x = 20 feet * tan(46 degrees)
Using a calculator, we have x ≈ 20 feet * 0.999980779, which is approximately 19.9996 feet.
Therefore, the distance from the base of the ladder to the building (x) is approximately 19.9996 feet.