JennyTheBest813
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Trigonometry
In the diagram, tan(C)=2.4. Find cos(A).
ONLY ANSWER IF YOU HAVE A VALID EXPLANATION!

Trigonometry In The Diagram TanC24 Find CosA ONLY ANSWER IF YOU HAVE A VALID EXPLANATION class=

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Corsaquix

Answer:

[tex]\cos(A)=\frac{12}{13}[/tex]

Step-by-step explanation:

Without loss of generality, let [tex]AB=24[/tex] and [tex]BC=10[/tex] (follows tan(C)=2.4). In a right triangle, the tangent of an angle is equal to its opposite side divided by its adjacent side and the cosine of an angle is equal to its adjacent side divided by the hypotenuse.

We can use the Pythagorean Theorem ([tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse) to solve for the hypotenuse:

[tex]24^2+10^2=h^2,\\h^2=676,\\h=26[/tex]

Therefore, [tex]\cos(A)=\frac{24}{26}=\boxed{\frac{12}{13}}[/tex]

helloIneedschoolhelp
Cos(A) = 12/13

Hope this helps
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