Question

consider the diagram shown where a ladder is leaning against the side of a building. the base of the ladder is 12 ft from the building. how long is the ladder? (to the nearest ft)

Explanation:

Step1: Identify adjacent side, angle

We know $\angle A = 70^\circ$, adjacent side $AC = 12$ ft, ladder length is hypotenuse $AB$.

Step2: Use cosine definition

$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$, so $\cos(70^\circ) = \frac{AC}{AB}$
Rearrange to solve for $AB$: $AB = \frac{AC}{\cos(70^\circ)}$

Step3: Calculate the value

Substitute values: $AB = \frac{12}{\cos(70^\circ)}$
$\cos(70^\circ) \approx 0.3420$, so $AB \approx \frac{12}{0.3420} \approx 35.09$
Round to nearest foot.

Answer:

35 ft