finding third point, provided two points , an angle and the length from one of two given points

Question

I have gone through many of the answers and I have not a suitable one so I am asking this question

As provide in the reference image I have been provide two points A(x, y) and B(x,Y), an angle Θ and length d from A(x, Y) to third point C(x,Y).

Basically I need to know how to calculate point C(x, y).

Please any help will be useful.

reference image

Answer 1

1) Find the length of \begin{equation} |AB|=\sqrt((x_1-x_2)^2+(y_1-y_2)^2 \end{equation} 2) Use the angle between $A$ and $B$ to find the value of the length between $B$ and $d$ line which is orhogonal and let's say that point $D$ \begin{equation} sin \theta = \frac{|BD|}{|AB|} \end{equation} 3) Use the Pisagor theorem to find the length between $B$ and $C$ points \begin{equation} |BC|^2=|BD|^2+|CD|^2 \end{equation} 4) Using the same idea given 1, find the $x$ and $y$ values for point $C$

Answer 2

You may find the slope of AC using the formula $$ \tan(\theta)=\frac {m_1-m_2}{1+m_1m_2}$$ Where $m_1$ is slope of $AB$ and $m_2$ is slope of $AC$

Then you can locate the point $C$ On the line $AC$ knowing the distance from $A$ to $C$