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.
x= 13.89 ft
x= 42.23 ft
x= 14.39 ft
x= 28.79 ft
To solve this problem, we can use the trigonometric relationship between the angle of elevation and the sides of a right triangle.
In this case, the ladder forms the hypotenuse of the triangle, and x represents the base of the ladder. We are given that the angle of elevation is 46°.
To find x, we can use the trigonometric function tangent (tan) which relates the opposite side (x) to the adjacent side (20 ft) using the formula:
tan(angle) = opposite/adjacent
tan(46°) = x/20
To solve for x, we can rearrange the equation:
x = 20 * tan(46°)
Using a calculator, we can find:
x = 20 * 1.0723687100246822
x ≈ 21.447 ft
Therefore, the correct answer is x ≈ 21.447 ft.
pick from my choices
Apologies for not selecting from your choices earlier. From the options you provided, the correct answer is:
x = 13.89 ft