Question

5.) a ladder that is 30 ft long needs to reach 27 ft up a building. what should the angle off of the vertical be?

Explanation:

Step1: Define the cosine relationship

Let the angle off - vertical be $\theta$. In a right - triangle formed by the ladder, the building, and the ground, the length of the ladder is the hypotenuse $c = 30$ ft and the height on the building is the adjacent side to the angle $\theta$ with respect to the vertical, $a = 27$ ft. We know that $\cos\theta=\frac{a}{c}$.

Step2: Substitute the values

Substitute $a = 27$ and $c = 30$ into the cosine formula: $\cos\theta=\frac{27}{30}=0.9$.

Step3: Find the angle

To find $\theta$, we take the inverse cosine of 0.9. So, $\theta=\cos^{- 1}(0.9)$. Using a calculator, $\theta\approx25.84^{\circ}$.

Answer:

$\theta\approx25.84^{\circ}$