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: Identify trigonometric ratio

We have a right - triangle where the adjacent side to angle $x$ is $4$ ft and the hypotenuse is $12$ ft. We use the cosine function $\cos(x)=\frac{\text{adjacent}}{\text{hypotenuse}}$. So, $\cos(x)=\frac{4}{12}=\frac{1}{3}$.

Step2: Solve for $x$

We know that $x = \cos^{- 1}(\frac{1}{3})$. Using a calculator, $x=\cos^{-1}(\frac{1}{3})\approx70.53^{\circ}$.

Step3: Check safety

Since $70^{\circ}<70.53^{\circ}<75^{\circ}$, the ladder meets safety standards.

Answer:

$x\approx71^{\circ}$
Yes