Question

riangular 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

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asked by King
Jan 10, 2020
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
sinAD/4 = 4/sinD
c) use the sine law
5/sin30 =4/DC
d) area = (1/2)(5)(4)sin

Answer 1

I see one error in my previous post to this, and it needs one clarification
change the following
D = 38.68°
So now you can find ∠BDA and ∠BAD and from there all remaining angles.
to
<b>D = 38.68° or 141.32° because the sine is positive in I or II.
But you said ∠BDC is obtuse , so make sure your diagram shows D as the obtuse angle
So now you can find ∠BAD and from there all remaining angles.</b>

The error is here: it should be
<b>b)for AD, use the sine law
AD/sin DBA = 4/sin38.68°</b>

Answer 2

What about length of DC