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https://vle.mathswatch.co.uk/images/questions/question1818.png

 Dec 9, 2018
 #1
avatar+98102 
+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

 

 

cool cool cool

 Dec 9, 2018
 #2
avatar+7 
+1

Thanks. It was right

HelpmeNow12  Dec 9, 2018
 #3
avatar+98102 
0

OK.....glad to help.....!!!

 

 

cool cool cool

CPhill  Dec 9, 2018

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