Answer
The distance from point A to point B equals $113.5$ yards
Work Step by Step
Let us notate with $c$ the distance from point A to point B in the triangle.
Then we can apply the law of cosines since we know what $a,b$ and $\gamma$ are.
$a = 105 $ yards, $b = 65$ yards and angle $\gamma = 80$ degrees.
We just need to plug in these values into the formula and we get our answer:
$c^{2} = a^{2}+b^{2}-2(ab) cos\gamma$
$c^{2} = 105^{2}+65^{2}-2(105*65)cos 80^{\circ}$
$c^{2} = 11025+4225-13650 * cos 80^{\circ}$
$c^{2} = 12879.7$
Then we just take the square root of 12879.7 and we have our answer:
$c = \sqrt {12879.7} $
$c = 113.5 $
