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14 votes
How can I use the figure to find the exact value?

How can I use the figure to find the exact value?-example-1
User Bakamike
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1 Answer

14 votes
14 votes

theoremGiven:-

A triangle.

To find:-


\cos (\alpha)/(2)

So now we use the formula,


\cos (\alpha)/(2)=\pm\sqrt[]{(1+\cos\alpha)/(2)}

Also,


\cos \alpha=\frac{Adjacent\text{ side}}{Hypotnews}

So we use Pythagoras theorms,


\begin{gathered} x=\sqrt[]{24^2+7^2} \\ x=\sqrt[]{576+49} \\ x=\sqrt[\square]{625} \\ x=25 \end{gathered}

So now we substitute,


\cos \alpha=(24)/(25)

So now we get,


\pm\sqrt[]{(1+\cos \alpha)/(2)}=\pm\sqrt[]{(1+(24)/(25))/(2)}=\pm\sqrt[]{((49)/(25))/(2)}=\pm\sqrt[]{(7)/(10)}

So the solution is,


\pm\sqrt[]{(7)/(10)}

User Imtee
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