Question

question 1 20 pts a 32 - foot tall ladder leans against a building. the ladders base is 15 feet from the building. find the angle that the ladder makes with the ground. found to the nearest tenth if necessary.

Explanation:

Step1: Identify the trig - ratio

We have a right - triangle where the length of the ladder is the hypotenuse ($c = 32$ feet) and the distance from the base of the ladder to the building is the adjacent side to the angle we want to find ($a = 15$ feet). We use the cosine function: $\cos\theta=\frac{a}{c}$.

Step2: Substitute the values

Substitute $a = 15$ and $c = 32$ into the cosine formula: $\cos\theta=\frac{15}{32}$.

Step3: Find the angle

$\theta=\cos^{- 1}(\frac{15}{32})$. Using a calculator, $\cos^{-1}(\frac{15}{32})\approx62.8^{\circ}$.

Answer:

$62.8^{\circ}$