The angle between the tangents drawn from the origin to the circle $(x-7)^2+(y+1)^2=25$ is

Equation of the circle: $(x-7)^2+(y+1)^2=25$ Center is at $(7,-1)$ with radius $r=5$. The tangents originate from the point $P=(0,0)$. Distance from $P$ to center is $d=\sqrt{(7-0)^2+(-1-0)^2}=\sqrt{49+1}=\sqrt{50}$. The tangent at any point is perpendicular to the radius at that point, forming a right triangle with sides $r=5$, $d=\sqrt{50}$, and tangent length. Let $\theta$ be the angle between the two tangents. Then $\sin(\theta/2)=r/d$. $\theta/2=\arcsin(5/\sqrt{50})=\arcsin(1/\sqrt{2})=\pi/4$ $\theta=2(\pi/4)=\pi/2$ radians Converting to decimal: $\pi/2\approx1.5708$ radians.