Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

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=

Sagot :

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]

Cos(A) = 12/13

Hope this helps