The figure below represents a triangular flower garden ABC in which AB = 4m, BC = 5and ∠BCA =30 degrees . Point D lies on AC such that BD = 4 m and ∠BDC is obtuse.

Question

The figure below represents a triangular flower garden ABC in which AB = 4m, BC = 5and ∠BCA =30 degrees . Point D lies on AC such that BD  = 4 m and ∠BDC is obtuse.
Find, correct to 2 decimal places:
(a) the length of AD;                                                                                       
(b) the length of DC;

oobleck · Accepted Answer

As I posted earlier,

calling the angle A,B,C as usual in a diagram, use the law of sines to find that
sin(∠BDC)/5 = sin(30)/4
so, sin ∠BDC = 5/8
But you want the obtuse angle.
Now you know that ∠BDA = 180 - ∠BDC
And, since triangle BDA is isosceles, ∠DAB = ∠BDA
Now you can find ∠B, and use the law of sines to find the other sides.
And recall that in any triangle ABC, the area = 1/2 ab sinC

So, where do you get stuck? Did you draw the triangle to get an idea what's going on?

King · Answer

Both. how to use law of sin (a) The length of AD; AD/4 = (b) the length of DC