Hello!
The answer is:
[tex]cos(R)=\frac{1}{2}[/tex]
Why?
Since it's a right triangle and we need to know the adjacent side of the triangle, in order to find cos(R), we can use the Pythagorean Theorem.
Pythagorean Theorem formula:
[tex]c^{2}=a^{2} +b^{2}[/tex]
Where:
[tex]c=hypotenuse=20\\a=FirstTriangleSide=AdjacentSide\\b=SecondTriangleSide=OppositeSide=10\sqrt{3}[/tex]
So, the adjacent side will be:
[tex]AdjacentSide=\sqrt{c^{2}-b^{2}}=\sqrt{20^{2}-(10\sqrt{3})^{2}}=\sqrt{400-100*3} \\AdjacentSide=\sqrt{100}=10[/tex]
Now, that we know the adjacent side, we can calculate cos(R), so:
[tex]cos(R)=\frac{AdjacentSide}{Hypotenuse}=\frac{10}{20}=\frac{1}{2}[/tex]
Have a nice day!
