So I had a math test and so far things went fine. Except from that one trigonometric problem where I wasn't able to score even 1 point. I'm also having a hard time finding something similar on the internet that's close to the trigonometric problem in the exam. Luckily, I still remember roughly all important numbers and words, so maybe someone is able to help me out.
A road goes between the village $A$ and $D$, which are both on the same horizontal plane. The road also goes through a tunnel, which starting point is $B$ and ending point is $C$. Because $A$ and $D$ can't be directly measured, there is a point $S$ on the same horizontal plane. The distance between $AS$ and $SD$ is:
$$AS = 1830 = a$$ $$SD = 1200 = b$$ $$\angle ASD = \alpha = 21.07^{\circ}$$ $$\angle CSD = \beta = 25.93^{\circ}$$ $$y = 108$$
How long is the road between $A$ and $D$?
and
How long is the tunnel between $B$ and $C$?
Does anyone how even a slight idea on how to approach this problem?
I mean, I would be able to calculate the missing sides, but I'm having a really hard time drawing the triangle to solve this problem.
Any input is appreciated!
Thanks in advance!