Question

a 12 - foot ladder is placed 4 feet away from a house as shown.
what is the value of x, rounded to the nearest degree?
x ≈
according to the manufacturer, if the angle the ladder forms with the ground, x, is between 70° and 75°, then it meets safety standards.
is this ladder being used safely?

Explanation:

Step1: Use cosine function

We know that in a right - triangle, \(\cos x=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, the adjacent side to angle \(x\) is \(4\) and the hypotenuse is \(12\). So, \(\cos x=\frac{4}{12}=\frac{1}{3}\).

Step2: Find the angle \(x\)

To find \(x\), we use the inverse cosine function \(x = \cos^{-1}(\frac{1}{3})\). Using a calculator, \(x\approx71.57^{\circ}\approx72^{\circ}\) (rounded to the nearest degree).

Step3: Check safety

Since \(70^{\circ}<72^{\circ}<75^{\circ}\), the ladder meets the safety standards.

Answer:

\(x\approx72^{\circ}\); Yes, the ladder is being used safely.