The value of cos C rounded to the nearest hundredth is 0.38.
What is a cosine of an angle?
In a right angle triangle the cosine of an angle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
What is Pythagoras theorem?
Pythagoras' theorem states that for all right-angled triangles, "The square on the hypotenuse is equal to the sum of the squares on the other two sides".
According to the given question
We have a right angled triangle ABC, in which right angle is at B.
Also,
BC = 15
AB = 36
[tex]AC = \sqrt{AB^{2}+BC^{2} }[/tex] (By Pythagoras theorem)
⇒[tex]AC = \sqrt{15^{2} +36^{2} }[/tex]
⇒[tex]AC = \sqrt{1521}[/tex]
⇒AC = 39
⇒ Hypotenuse of triangle ABC is 39.
Now, the adjacent side w.r.t ∠C is BC
Therefore, the cosine of an angle C is given by
[tex]cosC=\frac{BC}{AC}[/tex]
⇒[tex]CosC= \frac{15}{39} =\frac{5}{13}[/tex]
⇒[tex]cosC =0.38[/tex]
Hence, the value of cos C rounded to the nearest hundredth is 0.38.
Learn more about the cosine of an angle here:
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