Answer
$\approx165.3\text {yd}$
Work Step by Step
By the law of cosines: $c^2=a^2+b^2-2ab\cdot \cos(C)$, where $C$ is the included angle of $a$ and $b$.
Hence, if the distance between the ball and the center of the green is $x$, then:
$x^2=35^2+150^2-2(35)(150)\cos{110^\circ}\\x^2\approx27316.2115\\x=\sqrt{27316.2115}\\
x\approx165.3$
