Construct a hyperbolic triangle from $A$, $B$, and the center of the unit circle, $C$. Let $a$ be the length of $BC$, $b$ the length of $AC$, and $c$ the length of $AB$. Let $\alpha$, and $\gamma$ be the values of $\angle CAB$ and $\angle ACB$, respectively.
The value of $c$ is given as distance $d$:
$$c = d$$
The value of $\alpha$ is determined from the angle of $A$ relative to the unit circle, $\epsilon$; and the angle correspondent to the given direction of travel, $\delta$:
$$\alpha = |\pi - |\epsilon - \delta||$$
The value of $b$ can be determined based on the Euclidean distance from the center of the unit circle to $A$, $d_A$:
$$b = 2 \operatorname{arctanh}(d_A)$$
The value of $a$, the hyperbolic distance between $B$ and the center of the unit circle, can now be determined by the hyperbolic law of cosines:
$$cosh(a) = cosh(b)cosh(c) - sihn(b)sinh(c)\cos(\alpha)$$
$$a = arccosh(cosh(b)cosh(c) - sihn(b)sinh(c)\cos(\alpha))$$
The value of $C$ can be also be determined by the hyperbolic law of cosines:
$$\cos(\gamma) = \frac{cosh(a)cosh(b) - cosh(c)}{sinh(a)sinh(b)}$$
$$\gamma = arccos(\frac{cosh(a)cosh(b) - cosh(c)}{sinh(a)sinh(b)})$$
Now, add (or subtract), $\gamma$ from $\epsilon$ to determine the angle of $B$ relative to the unit circle, $\theta$. The Euclidean distance between $B$ and the center of the unit circle, $d_B$, can be determined using the exponential function:
$$d_B = \frac{e^a - 1}{e^a + 1}$$
Using this distance, the coordinates $x_B$ and $y_B$ of $B$ can be now be determined using basic trigonometric functions:
$$x_B = d_B \cos(\theta)$$
$$y_B = d_B \sin(\theta)$$
The coordinates of destination point $B$ are $(x_B, y_B)$.