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Answer:
69.5 degrees to nearest tenth.
Step-by-step explanation:
cos x = 7/20
x = 69.51 degrees.
The angle that the ladder makes with the ground is [tex]69.51^\circ[/tex] approximately.
What are the six trigonometric ratios?
Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.
In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).
The slant side is called hypotenuse.
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.
From that angle (suppose its measure is θ),
[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]
The ladder is of 20 feet and the base of the ladder is 7 feet from the base of the wall on which it is leaning.
Usually wall is vertical to the ground, so assuming it makes 90 degrees(ie being vertical).
We can simulate this situation approximately by a right angled triangle as shown in the image attached below.
The cos of angle that the ladder make with the ground is:
[tex]cos(\theta) = \dfrac{|AC|}{|BC|} = \dfrac{7}{20}[/tex]
Using inverse of cos ratio, we get the value of that angle (in degrees) as:
[tex]\theta = cos^{-1}(7/20)[/tex]
Using calculator and the fact that we use only that angle result which is < 90 degrees (so that sum of these angles doesn't exceed 180 degrees which is sum of angles of any triangle, as one angle of a right angled triangle is already 90 degrees), we get:
[tex]\theta \approx 69.51^\circ[/tex]
Thus, the angle that the ladder makes with the ground is [tex]69.51^\circ[/tex] approx
Learn more about inverse trigonometric functions here:
https://brainly.com/question/12551115
