Question

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

Answer 1

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)}`