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Math Help - What is cos A?

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    Exclamation What is cos A?

    Two legs of a right triangle are 2 and the square root of 5. Let angle Abe the smallest angle of triangle ABC. What is cos A?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jumpman23 View Post
    Two legs of a right triangle are 2 and the square root of 5. Let angle Abe the smallest angle of triangle ABC. What is cos A?
    you should draw a diagram and fill in what you know. ordinarily i would, but i'm not in the mood right now.

    let's find the hypotenuse first.

    By Pythagoras' Theorem:

    h^2 = 2^2 + \left( \sqrt {5} \right)^2
    where h is the length of the hypotenuse

    \Rightarrow h^2 = 4 + 5 = 9

    \Rightarrow h = \sqrt {9} = 3

    Now the smallest angle will be opposite the smallest side, that means it will be adjacent to the longest side (other than the hypotenuse). that means \sqrt {5} is the anjacent side to \angle A

    \Rightarrow \cos A = \frac {adj}{hyp} = \frac { \sqrt {5}}{3}
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