A 20-foot ladder leans against a wall so that the ladder's angle of elevation is 46°.
*. Find x, the distance from the base of the ladder to the building. B
We can use trigonometry to solve this problem.
Let x be the distance from the bottom of the ladder to the wall.
In the right triangle formed by the ladder, the wall, and the ground, the hypotenuse is the length of the ladder (20 feet), the opposite side is x, and the angle opposite x is 46°.
Using the sine function, we can write:
sin(46°) = x/20
To solve for x, we can rearrange the equation:
x = 20 * sin(46°)
Using a calculator, we can calculate sin(46°) ≈ 0.7193.
So, x ≈ 20 * 0.7193 ≈ 14.386 feet.
Therefore, the distance from the base of the ladder to the building is approximately 14.386 feet.