An angle, the bottom of the ladder makes with the ground is 73.74°.
Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a triangle (right-angled triangle) and its angles.
For the given situation,
The length of the ladder = 25 feet long
The vertical height from the base of the pillar to the top of the ladder = 24 feet
Let θ be the angle, that the bottom of the ladder makes with the ground.
The angle can be found by using the trigonometric ratio,
[tex]sin \theta = \frac{opposite }{hypotenuse}[/tex]
Here, opposite side = 24 feet and hypotenuse side = 25 feet
⇒ [tex]sin \theta = \frac{24}{25}[/tex]
⇒ [tex]sin \theta = 0.96[/tex]
⇒ [tex]\theta = sin^{-1}(0.96)[/tex]
⇒ [tex]\theta = 73.7397[/tex] ≈ [tex]73.74[/tex]
Hence we can conclude that an angle, the bottom of the ladder makes with the ground is 73.74°.
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