Question

question: 7
henry is painting a house. he placed a 24 foot ladder 15 feet away from the base of the house so that it leaned up against the house.
enter the measure of the angle that is formed between the ladder and the ground, rounded to the nearest tenth.

Explanation:

Step1: Identify the trigonometric ratio

We know the adjacent side ($a = 15$) and the hypotenuse ($c=24$) of the right - triangle formed. We use the cosine ratio: $\cos\theta=\frac{a}{c}$.
So, $\cos\theta=\frac{15}{24}=\frac{5}{8}$.

Step2: Find the angle

To find $\theta$, we take the inverse cosine (arccos) of $\frac{5}{8}$.
$\theta=\cos^{-1}(\frac{5}{8})$.
Using a calculator, $\cos^{-1}(\frac{5}{8})\approx51.3^{\circ}$.

Answer:

$51.3$