Harold is moving a 5- foot tall refrigerator. He tilts it onto its rear edge forming an angle between the back of the refrigerator and the floor; the top edge of the tilted refrigerator is exactly 4 feet above the floor as shown in the following diagram.
What is the cosine of the angle the refrigerator makes with the floor?
A, 4/5
B, 5/4
C, 4/3
D, 3/4
E, 3/5
Please help I’ll give branliest
Answers
The cosine of the angle the refrigerator makes with the floor is option (E) 3/5 is the correct answer.
What is trigonometry?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,
Harold tilted the 5 foot fridge, so the slanting height = 5 feet
The tilted refrigerator makes the height 4 feet from the floor.
From the diagram,
The three sides of the triangle according to Pythagoras theorem are
Hypotenuse side, h = 5 feet
Opposite side, o = 4 feet
Let a be the adjacent side.
By Pythagoras theorem,
[tex]Hypotenuse^{2} = Opposite^{2}+Adjacent^{2}[/tex]
⇒ [tex]5^{2} =4^{2} +a^{2}[/tex]
⇒ [tex]a^{2} = 25-16[/tex]
⇒ [tex]a=\sqrt{9}[/tex]
⇒ [tex]a=3[/tex]
Thus the trigonometric ratio cosine of the angle is
[tex]cos \theta =\frac{Adjacent}{Hypotenuse}[/tex]
⇒ [tex]cos \theta =\frac{3}{5}[/tex]
Hence we can conclude that the cosine of the angle the refrigerator makes with the floor is option (E) 3/5 is the correct answer.
Learn more about trigonometry here
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