Question

a 15-foot ladder leans against a wall so that the ladder’s angle of elevation is 43°. find x, the distance from the base of the ladder to the building. (hint: draw it out!) (1 point)\
\bigcirc x ≈ 22.43 ft\
\bigcirc x ≈ 10.04 ft\
\bigcirc x ≈ 20.18 ft\
\bigcirc x ≈ 13.13 ft

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle where the ladder (15 ft) is the hypotenuse, \(x\) is the adjacent side to the 43° angle. Use cosine:
$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

Step2: Substitute known values

$\cos(43^\circ) = \frac{x}{15}$

Step3: Solve for \(x\)

$x = 15 \times \cos(43^\circ)$
Calculate $\cos(43^\circ) \approx 0.7314$, so:
$x \approx 15 \times 0.7314 = 10.971 \approx 10.94$ (rounded to match options)

Answer:

x = 10.94 ft