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.

Question

x= 13.89 ft
x= 42.23 ft
x= 14.39 ft
x= 28.79 ft

Answer 1

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.

Answer 2

pick from my choices

Answer 3

Apologies for not selecting from your choices earlier. From the options you provided, the correct answer is:

x = 13.89 ft