Posted by **stranger** on Monday, April 8, 2013 at 8:49am.

Convex quadrilateral ABCD has sides AB=BC=21, CD=15 and AD=9. Given additionally that ∠ABC=60∘, what is the length of BD?

- Geometry -
**Reiny**, Monday, April 8, 2013 at 10:38am
Join the diagonals

Since B - 60° and AB = BC = 21

ABC must be equilateral and AC = 21

Now in triangle ACD we have 3 sides, and by the cosine law I found angle D to be 120°

interesting!

using the sine law in triangle ACD

sin CAD/15 = sin60/21

sin CAD = .61858..

angle CAD = 38.3232... (I stored that)

angle BAD = 60 + 38.32... = 98.21..°

by the cosine law:

BD^2 = 21^2 + 9^2 - 2(21)(9)cos BAD

= 528

BD = √528 or appr 22.98

- Geometry -
**Finalhero**, Wednesday, April 10, 2013 at 4:27pm
Reiny in the last step u have done an error as 21^2 =441 + 9^2 = 81 = 522

and 2*21*9*cos(98) = - 54.6

so 522 - (-54.6)=522+52.6=574.6

and square root of 574.6 = 23.97 ~ 24

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