#1**+1 **

Note that angle C = 180 - (38 + 44) = 180 - 82 = 98°

Using the Law of Sines, we can find DC as

DC / sin 38 = BD / sin 98

DC = 10 *sin 38 * sin 98 ≈ 6.097

And the area of BCD can be found as

(1/2) DB * DC sin BDC = (1/2) *10 * 6.097 sin 44 ≈ 21.18 units^2 (1)

And angle ABD = 90 - 55 = 35°

Using the Law of Sines again

BD/sin A = AD / sin ABD

10/ sin 90 = AD /sin 35

AD = 10 sin 35 ≈ 5.74

And the area of ABD can be found as

(1/2)BD * AD *sin ADB =

(1/2) 10 * 5.74 sin 55 ≈ 23.5 units^2 (2)

So....the total area = (1) + (2) = [ 21.18 + 23.5] units^2 ≈ 44.68 units^2 = 44.7 units^2

CPhill Dec 9, 2018