Question

xin leans a 26 - foot ladder against a wall so that it forms an angle of 78° with the ground. whats the horizontal distance between the base of the ladder and the bottom of the wall? round your answer to the nearest hundredth of a foot if necessary.

Explanation:

Step1: Define adjacent side relation

We use cosine: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$, where $\theta=78^\circ$, hypotenuse = 26 ft, adjacent = horizontal distance $x$.

Step2: Rearrange to solve for $x$

$x = 26 \times \cos(78^\circ)$

Step3: Calculate the value

First, $\cos(78^\circ) \approx 0.2079$, so $x \approx 26 \times 0.2079$
$x \approx 5.4054$

Answer:

5.41 feet