Find cos(a) in the triangle.

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Find cos(a) in the triangle.

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Answer:

cos(α) = 24/25.

Step-by-step explanation:

First of all, we'll find the answer just using the fact that ABC is a right triangle in C. So, by the definition of cosine:

\cos(\alpha) = \dfrac{AC}{AB}\\\\\boxed{\cos(\alpha) = \dfrac{24}{25}}

Now, we'll solve the question with another approach. By the Law of Cosines in the triangle ABC:

BC^2 = AB^2+AC^2-2\cdot AB\cdot AC\cos(\alpha)\\\\7^2 = 25^2+24^2-2\cdot 25\cdot 24\cos(\alpha)\\\\49 = 625+576-1200\cos(\alpha)\\\\1200\cos(\alpha)=1152\\\\\boxed{\cos(\alpha) = \dfrac{24}{25}}

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Aubrey Bechtelar
15.5k 3 10 26
answered 9 months ago