Answer:
62.182°
Step-by-step explanation:
Using cos and sin you are able to find the height of the ladder from the bottom of the house to the place the top of the ladder is. You can do this by making a triangle. By using the lengths and angles already present you are able to find all angles of the triangle.
The angle at which the ladder is leaning is 62.18°.
Trigonometry is the branch of mathematics that deals with calculating the angles of triangles or the lengths of their sides. It mainly concerned on the properties of right angled triangle.
For the given situation,
The length of the ladder = 15 feet
The distance between the house and the ladder base = 7 feet
The angle at which the ladder is leaning can be found by using trigonometric ratio, cos θ.
we know that, [tex]cos[/tex] θ = [tex]\frac{Base}{Hypotenuse}[/tex]
The figure below shows the relationship between the sides.
⇒ [tex]cos[/tex] θ = [tex]\frac{7}{15}[/tex]
⇒ θ = [tex]cos^{-1}(\frac{7}{15} )[/tex]
⇒ θ = [tex]62.18[/tex]
Hence we can conclude that the angle at which the ladder is leaning is 62.18°.
Learn more about trigonometry here
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