Question

a 20-foot ladder leans against a wall so that the ladders angle of elevation is 46 degrees. find x, the distance from the base of the ladder to the building. (1 point)
x = 43.23 ft.
x = 28.79 ft.
x = 14.39 ft.
x = 13.89 ft.

Explanation:

Step1: Identify trigonometric ratio

We use cosine, since $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta=46^\circ$, adjacent side is $x$, hypotenuse is 20 ft.

Step2: Set up the equation

$\cos(46^\circ) = \frac{x}{20}$

Step3: Solve for x

Rearrange to isolate $x$: $x = 20 \times \cos(46^\circ)$
Calculate $\cos(46^\circ) \approx 0.6947$, so $x \approx 20 \times 0.6947 = 13.89$

Answer:

X = 13.89 ft.