For what positive value of $t$ is $|6+ti| = 10$?
I know that $|6+ti|$ represents the magnitude of the complex number $6+ti$, which is the distance from the origin to the point $(6,t)$ on the complex plane. I can use the Pythagorean theorem to relate this magnitude to the real and imaginary parts: $|6+ti|^2 = 6^2 + t^2$. Since I want $|6+ti| = 10$, I can square both sides and get $10^2 = 6^2 + t^2$. Simplifying, I get $100 = 36 + t^2$. Subtracting $36$ from both sides, I get $64 = t^2$. Taking the square root of both sides, I get $\pm 8 = t$. However, the problem asks for a positive value of $t$, so I can discard the negative solution and conclude that $t = 8$. 