The measure of the value of x is 70.52 degrees.
Given
A 12-foot ladder is placed 4 feet away from a house as shown.
According to the manufacturer, if the angle the ladder forms with the ground, x, is between 70° and 75°, then it meets safety standards.
The cos theta is defined as the ratio of the side adjacent to the angle and the hypotenuse.
The following formula is used to calculate the value of x;
[tex]\rm Cosx=\dfrac{Side \ adjacent \ to \ angle}{Hypotenuse}\\[/tex]
Where the side adjacent to angle = 4 and hypotenuse is 12.
Substitute all the values in the formula;
[tex]\rm Cosx=\dfrac{Side \ adjacent \ to \ angle}{Hypotenuse}\\\\\rm Cosx=\dfrac{4}{12}\\\\\rm Cosx=\dfrac{1}{3}\\\\x=Cos{-1}(\dfrac{1}{3}\\\\x= 70.52 \ degrees\\\\[/tex]
Hence, the measure of the value of x is 70.52 degrees.
To know more about Trigonometric ratios click the link given below.
https://brainly.com/question/3630461
Answer:
71
Step-by-step explanation:
Yes, the ladder is being used safely
