triangular flower garden ABC in which AB = 4m, BC = 5and ∠BCA =30. Point D lies on AC such that BD = 4 m and ∠BDC is obtuse.
Find:
(a) ∠BDC
(b) the length of AD
(c) the length of DC
(d) the area of the flower garden ABC
If you made a reasonable sketch you will see that ∆ABD is isosceles and you are given that
∠BDC is obtuse.
Look at ∆BCD, you can use the sine law to find ∠BDC
sin D/5 = sin 30°/4
sinD = 5(1/2) / 4 = 5/8
D = 38.68°
So now you can find ∠BDA and ∠BAD and from there all remaining angles.
b) for AD, use the sine law
c) use the sine law
d) area = (1/2)(5)(4)sin ∠ABC