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What is the value of cos A

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The give diagram represents a right angled triangle with side AB and BC as follows,


\begin{gathered} AB=24 \\ BC=7 \end{gathered}

Apply the Pythagoras Theorem and solve for the hypotenuse,


\begin{gathered} AC^2=AB^2+BC^2 \\ AC^2=(24)^2+(7)^2 \\ AC^2=576+49 \\ AC^2=625 \\ AC=\sqrt[]{625} \\ AC=25 \end{gathered}

Now, apply the cosine ratio for angle A as follows,


\begin{gathered} \cos A=(AB)/(AC) \\ \cos A=(24)/(25) \end{gathered}

Thus, the cosine of angle A is equal to 24/25 .

User Francesco S
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